Game Theory

Game Theory

Game theory is the study of the ways in which  the interaction options  of  economic factors  produce results  in respect of  Preferences  (or  facilities) of these customers, where they can be the target of the results in question by any of the agents. The meaning of this statement not be clear for non-experts until it is explained each of the italicized words and phrases and appeared in some of the examples. Doing this will be the main work of this article. First, however, we offer some historical and philosophical context in order to stimulate the reader the next work of art.

1. motivation philosophical and historical

He invented the mathematical theory of games by John von Neumann and Oskar Morgenstern (1944). For reasons that will be discussed at a later time, restrictions under which the sports theory initially apply only under special and limited circumstances. This situation has changed dramatically, we will study ways as we move forward, over the past six decades, as has been the deepening of the frame and dissemination. And continue to make improvements, we will review some of the outstanding problems which are located along the front edge push these developments towards the end of the article. However, at least since late in the 1970s it was possible to say with confidence that the game theory is the most important tool and useful in several analyst whenever they encounter situations in which what is considered the best action one factor (her) depends on expectations about what one or more other factors It will do, and what is considered their best work (for them) similarly rely on the expectations of them.

Although the game theory was presented mathematically and logically systematically only since 1944, and visions of game theory can be found among commentators dating back to ancient times. For example, in two of the texts of Plato,  and Lakas  Symposium, Socrates remember an episode of the battle Daleom that some commentators have interpreted (perhaps anachronistically) as involving the following situation. Consider a soldier at the front, waiting with his comrades to repel the enemy attack. It may occur to him that if the defense is likely to be successful, it is very likely that the personal contribution will be necessary. But if he stays, it is in danger of being killed or wounded, apparently any point. On the other hand, if the enemy is going to win the battle, then his chances of death or injury is higher, and now it is quite clear that no point, where the line will be overwhelmed anyway. Based on this logic, it seems that the soldier is better off escape regardless of who will win the battle. Of course, if all of the soldiers why this road as they all seem to    be, they are all in identical positions, this certainly achieve  results in that lost the battle. Of course, this point, because it happened to us as analysts, can also happen to the soldiers. Is this gives them a reason to stay in office? Just the contrary: the more fear increased the soldiers that will be lost the battle, and increase their incentives to get themselves out of harm’s way. The more the faith of the soldiers who will determine the winner in the battle, without the need for contributions to any particular person, and they have less reason to stay and fight. If every soldier  expects  this kind of thinking on the part of others, and all the mind quickly themselves in a state of panic, terrified of their leader they will have his hands to defeat the enemy before he fired a single shot.

Long before the game theory has come along analysts how to think in this type of problem to show systematically, there were some actual military commanders and affected their strategies. And thus the Conqueror Cortez, the Spanish, when landing in Mexico with a small force which was good reason to fear its ability to repel the attack of more numerous much of the Aztecs, remove the risk that his forces might think their way into retreat by burning ships on which had fallen. With the decline after and thus virtually been impossible, and Spanish soldiers was not the best course of action but to stand and fight and moreover, to fight with a lot of determination they can muster. Better yet, from the point of Cortez’s point of view, and his work it was a discouraging effect on the motives of the Aztecs. To burn his ships very clearly took care, so the Aztecs have to be sure to see what he had done. And then reasoned as follows: any leader who can be confident and so deliberately to destroy his option to be wise if the battle went badly for him must have good reasons for this extreme optimism. (Whatever can not be wise to attack an opponent who has a good reason, exactly, may be) for being sure that he can not lose. And thus the Aztecs fell in the surrounding hills, and Cortez was won without bloodshed.

These two cases, in Daleom and also manipulated by Cortez, has a logic behind the common and interesting. Note that the soldiers are not motivated to decline  only, or even primarily, through a rational assessment of the risks of battle and self-interest. Instead, they discover sound reason to run away from the realization that what was logical for them to do depends on what will make sense For others do, and that each of the other to note that as well. It may prefer even very brave soldier to run rather than heroic, but aimless, die in an attempt to stem the tide advent all by himself. Thus, we can imagine, without contradiction, the conditions in which an army, all Members who are brave, run away at full speed before the enemy makes a move. If the soldiers really are courageous, then this is certainly not the result of any of them you like. All prefer that we all stand and fight. What we have here, then, is the situation in which  the interaction of  many individually rational decision-making one and process operations for each soldier, produces the desired result by anyone. (Most armies in an attempt to avoid this problem completely as Cortez did because they can not usually make the retreat. physically impossible, it makes it  economically  impossible: that shoots fleeing and then stand up and fight is of course all rational soldier individually to work after all, Operating cost for is sure to be at least the same level of cost of stay).

It was found on another classic source, which calls this chain of logic in Shakespeare’s  Henry V. During the Battle of Agincourt, Henry decided to slaughter his French prisoners, in full view of the enemy and to the surprise of his subordinates, who described the action as being out of moral character. Henry gives hints at the reasons for the non-strategic considerations: he fears that the prisoners may liberate themselves and threatens his position. However, the game theorist may have equipped him with a complementary strategy (and prudential Similarly, although perhaps not moral) justification. His special forces note that the prisoners had been killed, and we note that the enemy may notice this. So, I know what fate will await them in the hands of the enemy if you do not win. Metaphorically, but very effectively, they have been burning their boats. The slaughter of prisoners sent a reasonable signal to the soldiers of both sides, and therefore change their own incentives in ways that favored English prospects for victory.

These examples may seem relevant only to those who find themselves in sordid cases of cut-throat competition. Perhaps, one might think, it is important for the generals, politicians and mafia men athletes, coaches and others who involve strategic manipulation of other jobs, but the philosopher must condemn her only immoral. Such a conclusion would be premature too, however. The study of  logic  that governs relations between incentives and strategic interactions and the results were key in modern political philosophy, since centuries before anyone had a clear name for this kind of logic. Share with philosophers and social scientists on the need to be able to represent and model systematically not only what people think normatively  should  do, but what often  actually do in interactive situations.

Hobbes  and Leviathan  is often considered work in the founding of the modern political philosophy, and the text that the continuation of the tour began to function and the justification for the state to impose restrictions on individual freedoms analyzes. Hobbs essence of logic can be given directly as follows. The best situation for all people is that each one is free to do as she pleases. (One may or may not agree with this as a matter of psychology, but it is a presumption of Hobbes). And often, and this is a free people willing to cooperate with each other for the implementation of projects that would be impossible for an individual working alone. But if there are any factors immoral or unethical around, they will notice that their interests may be at least in some cases better by getting the benefits of cooperation and not to be returned. Suppose, for example, you agree to help me build my house in exchange for my promise to help you build yours. After the completion of my house, and I can make your work to me for free simply by reneging on his promise. And then we realize, however, that if this leaves you with any home, you will have an incentive to take mine. This put me in constant fear of you, and force me to spend some precious time and resources guard myself against you. I can best reduce these costs by hitting the first and kill you at the first opportunity. Of course, you can expect all of this logic to me before, and so have a good reason to try to beat me to the punch. Because I can not be expected  this  logic by  you, the original fear was not paranoid. And you had me. In fact, not one of us actually needs to be unethical for this series of mutual Go logic. I think we need just that there is some  possibility  that some people may try to cheat in the transactions. Once a small wedge of doubt enters any one’s mind, the incentive caused by fear of the consequences that preceded -hit before it reaches the first quickly becomes overwhelming on both sides. If any one of us has any resources from our side that the other party may want, this deadly logic can take hold long before we silly to imagine that we could ever actually get as contract deals to help each other build homes in the first place . Left to their own computers, and the agents who are at least in some cases, narrow self-interest will repeatedly fail to reap the benefits of cooperation, and will live instead in a “war of all against all,” and words Hobbs. In these circumstances, and human life, as he clearly famously put it, it would be “solitary, poor, nasty, brutal and short.”

Hobbs was proposed solution to the problem of tyranny. People can hire an agent and one in the government whose job is to punish anyone who violates any promise. As long as the threatened punishment is severe enough, then the cost of reneging on promises to exceed the cost of maintaining them. Logic here is similar to those used by the army when he threatens to shoot deserters. If all people know that these incentives contract to most other countries, and cooperation will not only be possible, but it will be the standard expected, and the war of all against all become public peace.

Hobbs pushes the logic of this argument to the very strong conclusion, arguing that only a government with the right and the power to impose cooperation does not mean, however, the government is divided, “the arbitrary will of the ruler and one should impose an absolute obligation on the whole. Some contemporary political theorists believe that the specific steps that Hobbs the causes of his way to this conclusion is both safe and suitable. work through these issues here, however, will carry us away from our theme in the details of political philosophy contractarian. What is important in the current context is that these details, as they are actually used in the discussions contemporary, all of which involve a sophisticated interpretation of issues using modern game theory resources. Moreover, the most fundamental point Hobbes, that the main justification for the authority and practices of forced governments is “the need to protect themselves from what he calls the theorists game social dilemmas peoples”, and supported by many, Most political theorists and it was not. Note that Hobbs has not argued that tyranny is something desirable in itself. structure of his argument is that the logic of strategic interaction leaves only two possible general political results: tyranny and chaos. Agents reasonable then choose tyranny as the lesser of two evils.

Logic of Athenian soldiers, Cortez, politicians and agents Hobbs has a sound logic, one derived from their situation. In each case, the side of the environment that is most important to achieve the dealers of the results is their preferred set of expectations and reactions of potential strategies by other agents. Discrimination between behave  parametrically on the negative and the world of work  is  parametrically- to the world who is trying to act in anticipation of these measures is essential. If you want to kick a rock down the hill, you need concern yourself with a nearby rock in the media on the strength of your blow your only, and the extent of bonded with the supporting surface, the slope of the land on the other side of the rock, and the expected impact of the collision on foot. Each of these variables is independent of the values ​​of the plans and intentions, because the rock has no interests of its own, and takes no actions to try to help or frustrate you. By contrast, if you want to kick someone down the hill, then unless such person is unconscious, bound or unable Otherwise, you probably will not succeed unless you can hide your plans until it is too late for him to take any action evasive or frustration . Moreover, it should be expected that the cost of visiting you, and that it would be wise to consider possible responses to do. Finally, the relative probabilities of the responses depends on the expectations about possible responses to your answers. (Consider the difference it will make to both your reasoning if an armed one or both of you, or one of you is greater than the other, or one of you is the other coach.) Logical and issues associated with the second type of situation (kicking someone in exchange for the Rock) are usually much more complex, and simple hypothetical example and clarify.

Let’s assume first that you want to cross the river which spanned three bridges. (Let’s assume that swimming, wading or boating across from impossible.) It is known that the first bridge to be safe and free of obstructions. If you try to cross there, and you will succeed. The second bridge is located under the slope of large rocks which sometimes fall. And it lives by the third deadly cobra. Now suppose you want to arrange the order of the three bridges in respect of preference as transit points. What did not get to enjoy the positive risk your life, which, as a human being, you may, of complications we will take later in this article problem-then your decision is clear and explicit. The first bridge is clear that the best, because it is the safest. System to arrange the other two bridges, you need information about the relative levels of risk. If you can study the frequency of rock falls and Cobra movements for awhile, you may be able to calculate the likelihood of your being crushed rock in the second bridge is 10% and a raid on a cobra in the third bridge is 20%. Your logic here is precisely because it does not border the rocks nor cobra trying to influence your actions, through, for example, to hide the typical patterns of behavior because they know you’re studying them. It is clear what you should do here: a safe crossing the bridge. Now let’s complicate the situation a little. Suppose that the bridge with rocks and immediately before that, while it was difficult to raise the bridge safe for one day upstream. Situation your decision making here a little more complicated, but it is still a border accurately. You will have to decide whether the cost of long high value of the exchange to the death of a 10% chance of a stone. However, this is all you must decide, and the possibilities of your successful crossing is entirely up to you. The environment is not interested in your plans.

However, if we now complicate the situation by adding an element it is a border, it becomes more challenging. Suppose you are a fugitive of some kind, and are waiting on the other side of the river with a gun is your pursuer. She’ll catch and shoot you, let’s assume, unless they are waiting for when I tried to cross the bridge. Otherwise, you will flee. You can also mind through your choice of the bridge, it happens to you it was over there trying to anticipate your logic. It will seem so, certainly, choose a safe spot on the bridge would be a mistake, because that is just where they’ll expect you, and your chances of rising to the dead certainty. So maybe you should risk the rocks, because the odds are much better. But wait … if you can reach this conclusion, the private Chaser, which is just a rational and well-informed as you are, you can expect that you will reach it, and we will wait for you if you run away from the rocks. So maybe you should take your chances with a cobra. This is what they must not expect. But, then, do not … If you expect that you would not expect that they will not expect this, and then she’ll expect most of that. This dilemma, I realized with dread, is the year: You must do what you expect at least your pursuer. But no matter how I was more expecting her to not automatically expect it is what she will most expected. It seems to be trapped in the frequency. All of this has little to console you here is that, on the other side of the river, and were trapped Chaser your exactly in the same predicament, unable to make a decision and bridge waiting for in as soon as they imagined committing one, she will notice that if they can find The best reason to choose the bridge, you can expect that same reason and then avoid them.

We know from experience that in such cases, people usually do not stand and frequency in circles forever. As we will see later, there  is  a rational solution to this is, at best rational action available to both players. However, until the 1940s philosophers and economists do not know how to find them mathematically. As a result, economists have had to treat non-parametric effects as if they were complications on that border. This is likely to strike the reader as odd, since then, we have an example of the problem of crossing the bridge was supposed to show up, and non-parametric features are often basic features of the decision-making problems. Part of the explanation in a relatively late entry in the field of game theory lies in the problems that economists historically concerned. Some mainstream economists such as Adam Smith and David Ricardo, was mainly interested in the question of how agents in very large markets all nations can interact so as to achieve maximum monetary wealth for themselves. Smith fundamental insight, that is the best to maximize efficiency by agents seeking bargains freely mutual benefit, it has been verified mathematically in the twentieth century. However, the demonstration of this fact applies only under the “full competition”, that is, when faced with individuals or companies any costs of entry or exit to the market, and when there is no economies of scale, and when the measures are not agents have unintended side effects on other factors well-being. Economists always recognize that this set of assumptions idealization is purely for the purposes of analysis, not a possible state of affairs can anyone tries to (or should want to try) to achieve them. But even the mathematics of game theory matured near the end of the 1970s, economists hope that the closer market  close to  full competition, the more efficient it will be. There is no such hope, however, can mathematically or logically justified in general; in fact, as mainstream strict showed assumption to be false as far back as the 1950s.

This article is not about the foundations of the economy, but it is important to understand the origins and scope of game theory to know that full competition markets have been built to a feature that makes them susceptible to parametric analysis. Because agents facing any market entry costs, it will open a store in any given market until competition pays all profits to zero. This means that if production is fixed foreign demand and costs, and agents do not have a choice about how much to produce if they are trying to maximize the differences between costs and revenues. And these levels can be determined separately for each production factor, so it does not need to pay attention to what other people are doing. Each agent treats her counterparts from negative environmental features. Another type of situation that can be applied to classical economic analysis without resorting to game theory is that the monopoly faces many customers. Here, not as long as the customer has a large share of the demand enough to exert strategic influence, and lower non-parametric considerations and mission of the company is the only one to determine the combination of price and quantity of production that maximizes profits that. However, competition is both perfect and monopolistic arrangements are very special and unusual in the market. Before the advent of game theory, so, economists were very limited in the category of conditions that can be applied accurately models.

Share with philosophers, economists professional interest in the terms and techniques to maximize human welfare. In addition, the philosophers have a special concern with the rationale of the procedure, and must be justified in many cases, actions by reference to the expected results. (One tradition in philosophy, utilitarian, and is based on the idea that all actions are justified and must be justified in this way.) Without game theory, all of these problems wherever resistance analysis is a border aspects are relevant. Soon we will show this by reference to the most famous (though not the most common) for the game, the so-called  dilemma of the prisoner, and the other more typical, and games. In doing so, we will need to enter and to identify and clarify the essential elements of the theory and techniques of the game. In this work and therefore we move on now.

2. Basic elements and assumptions of game theory

2.1 Help

Economic factor is, by definition, an entity with preferences. Game theorists, such as economists and philosophers who study decision-making rational, and this description by an abstract concept called utility. This refers to some arrangement, and to a certain range, from self-care or change in self-care agent that is derived from the object or event. By ‘well-being’ we refer to some benchmark relative well-being, justified by reference to the context of the background work. For example, we have relative care for the countries of the evaluation (which we were agents for some purposes may model) by reference to the capita income, we relative care for the animal may assess, in the context of predicted and explained to her behavioral dispositions, by reference to the physical evolutionary expected fitness. In the case of people, it is most common in the economy and applications of game theory to assess the relative care by reference to their own judgments express or implied it. This is why we referred to above  Resume social welfare. Look at the person who loves the taste of pickles, but hates onions. It can be said to associate with the highest interest of the world that, that all things being equal, she would consume more of pickles less than with countries that were consumed more than a few onions, pickles and onions. Examples of this type suggests that the “benefit” shows on a personal scale  psychological fulfillment, and this is actually how they were interpreting the concept of origin by economists and utilitarian philosophers of Jeremy Bentham affected. However, economists in the early 20th century clearly growing recognition that the key was in their interest in the real estate market diminishing marginal demand, regardless of whether it was produced by individuals satiated consumers or some other factor. In the 1930s this motive of economists fit comfortably with the dominance of behavioral and experimental radical in psychology and philosophy of science, respectively. Behavioral and experimentalists extreme objected to the use of theoretical for these entities unobservable as’ crops of psychological fulfillment. “He was the intellectual climate and thus receptive to efforts economist Paul Samuelson (1938) to re-interest is defined in such a way that it becomes the concept of a purely technical and not one rooted in psychology speculation. Since becoming re standard in the 1950s Samuelson definition, when we say that the agent is acting so as to maximize the benefit to her, we mean “benefit” simply everything that is suggesting the agent her behavior to act consistently so as to make more likely. If this sounds circular to you, it must: theorists who follow Samuelson  intend  statement “agents behave so as to maximize their utility ‘as a tautology, where for” (Economic) Agent “any entity can be accurately described as working to maximize the function of the tool, a” work “is any selection-maximizing benefit from a range of possible alternatives, and a’utility function ‘is more than an economic factor. Like other redundancy that occurs in the foundations of scientific theories, and this interlocking system (recursive) definitions are not useful in itself, but because it helps to repair our investigation contexts.

Although the behavior of the 1930s and since then have been displaced because of the widespread interest in the cognitive processes underlying, many theorists still to follow the road Samuelson to understand the benefit because they believe that it is important to game theory applies to  any  type of agent person, bear, bee’s , a company or a country, not only to customers with human brains. When these theorists say that agents behave so as to maximize their usefulness, they want to be part of the  definition of  what it is to be an agent, and not empirical claim about possible internal states and motives. Pregnancy Samuelson of interest, which is known by preference detection theory  (RPT) presented his paper in classic (Samuelson (1938)) to meet this demand.

Economists and others who interpret the game theory in terms of RPT should not be thinking about game theory as it is in any way a demo account of the motives of some flesh and blood actors (such as actual people). Instead, it should be regarded as game theory as a part of the body of mathematics that are used to model these entities (which may or may not exist literally) who always identify the elements of the working groups of mutually exclusive, resulting in patterns of options, which, allowing for some stochasticity and noise, and can be modeled statistically as to maximize the utility functions. On this interpretation, the game can not disprove any theory of experimental observations, because they are not experimental theory in the first place. Of course, observation and experience for the benefit of a person who performs this interpretation to the conclusion that game theory is of little  help  in the description of the actual human behavior.

Some other theorists understand the point of game theory differently. They see game theory to provide an illustrative account of strategic thinking. This idea viable, we must assume that agents do at least sometimes what they do in nonparametric settings    to the theory of the game logic some procedures, such as those “rational recommend.” This understanding of the theory of the game include  standard  side, because «rational» is taken to indicate the property that an agent should at least generally want to be. This very general ways of thinking about the possible uses of the theory of the game compatible with the interpretation of a tautology of utility maximization. Not idle philosophical difference from the standpoint of game action scene, however. As we will see in the later part, those who hope to use game theory to explain the strategic    logic, rather than just strategic behavior, facing some of the philosophical and practical problems.

Since the theory of the game is a technique for modeling the official, you must have a device to think in terms of maximizing the benefit of sports. This device is called a  function tool. We will provide the general idea of the function of the tool during a special case of  hierarchy  utility function. (Later, we will experience the same benefits that include more information functions.) Called on the map of interest for an agent and’ozivh ‘because it maps  is Preferences  on the real numbers. Suppose that the agent  tenth  preferred package for the package  B and bundle  B  package c. We then set this on the list of numbers, where the maps function highest ranking package, the largest number in the list, the second-highest ranking pack at the following number largest in the list, and so on, and thus:

Pack  of  »3

Bundle  b  »2

Package  c  »1

The only property that painted this is the function of the system. Ingredients numbers are irrelevant. That is, it should not be inferred that the  Q  gets three times the amount of the benefit package    of the package they get from c. Thus, we can represent  exactly the same  function as the expediency above

Package and »7326

Bundle  b  »12.6

Package  c  »-1000000

Ordinal numbers housed in the utility function and therefore does not measure any  amount  of anything. A utility functions that the amounts  do  so-called issue of ‘Cardinal’. Whenever someone refers to the function of the tool without specifying any kind is meant, we must assume that ordinal. These are the types we will need for the first set of games we’ll examine. Later, when we come to see how to solve the games involving the  distribution of random, we have a game to cross the river from Part 1 above, for example, we’ll need to build facilities essential functions. This technology was given to do so by  von Neumann and Morgenstern (1944), and was a key aspect of the invention game theory. At present, however, we will need to functions ordinal only.

2.2 games and rationality

All cases in which agent and at least one can only work to maximize the benefits through pre-empt (either consciously or implicitly only in his behavior) responses to his actions on the part of one or more of the other factors and called the game. It referred agents involved in the Games on behalf of the players. If all agents and procedures optimal regardless of what others are doing, as is the case in a border cases purely or monopoly or perfect competition conditions (see  Section 1  above), we can model this is subject to appeal to the theory of the game, otherwise, we need it.

The game theories assume that the players have capabilities which are usually referred to in the literature of economics as a “rational”. This usually formulated by simple phrases like “assumes that the players are rational.” Literature in cash to the economy in general, or for the import of game theory in humanitarian disciplines, and this kind of rhetoric has become a powerful attraction for the attack. There are dense and complex web of related to “rationality” in the Western cultural tradition communications, and the word is often used to marginalize the standard properties as usual and the importance of passion and compassion and femininity. Game theorists use of the concept is not necessary, and generally do not, implicate this ideology. For present purposes we will use “economic rationality” as a purely technical, not a standard, the term to refer to a specific and narrow set of restrictions on preferences that are shared by von Neumann and the original version of the game theory, and RPT Morgenstern’s. Economists use in the second, and equally important (to them) the concept of rationality when markets are developed, which they call “rational expectations models”. In this phrase, «rational» does not refer to restrictions on preferences but  non -restrictions information: rational expectations is the ideal beliefs that accurately reflect the use of statistically weighted average of all the information available to the agent handling. The reader should note that these two uses of a single word in the same discipline is not linked technically. Moreover, the original RPT been identified over the years by many different sets of axioms for the purposes of the various modeling. Once you have decided rational treatment of the technical concept, every time we adjust the axioms we adjust the effectiveness of this concept. As a result, in any discussion involving economists and philosophers together, we can find ourselves in a situation where everyone uses the same word to refer to something different. Readers of the new economy, game theory, decision theory and the philosophy of work, this situation presents a challenge naturally.

In this article, “economic rationality” and will use the common technical sense within the game theory, microeconomic theory and formal resolution, as follows. Logical player in economic terms is the one who can (i) the evaluation of results, meaning the rank order in respect of their contributions in her care. (B) calculate the paths to the results, in the sense to recognize the sequence of actions that are related to potentially that results; and (c) determine the actions of groups of alternatives (which we described as ‘selection’ procedures) which achieved its most preferred results, due to the actions of other players. We may summarize the intuition behind all of this is as follows: Like an agent rational useful entity economically to the extent that they have alternatives, and choose from among this manner is driven, at least more often than not, through what seems best for their purposes. (For readers who are familiar with the anteriorly with the work of the philosopher Daniel Dennett, we can equate the idea of an agent economically rational with this type of entity Dennett characterize as  deliberate, and then say that we can predict the useful behavior agent economically rational of “deliberate attitude “.)

It may in some cases be satisfied with economic rationality through internal audit carried out by the agent, and they may or may not be aware computing or after taking into account the conditions and effects. In other cases, it may simply be embodied economic rationality in behavioral dispositions built by natural selection, cultural or market. In particular, in the procedure ‘chosen’ we call implicit and necessary deliberations, conscious or otherwise. Here we are talking about just that this action was taken when he was an alternative available in some sense “available”, which is usually set up the context of a specific analysis procedure. (‘Available’, as used by the game and economists theorists, it should never be read as if it means just a “metaphysical” or “logically” available; it is almost always practical, contextual and revisable endlessly through modeling more precise).

Each player in the game is facing a choice between two or more possible strategies. Strategy is to ‘play program “in advance to tell her what actions to take in response to  every possible strategy may be used to players other important italics phrase here. Will become clear when we sample some of the games below.

One of the crucial aspects of the specifications for the game includes information that the players have when choosing strategies. The simplest games (from the point of the logical structure of view) are those agents  and information is complete, and this means that at every point where he says each agent have a strategy to take action, and she knows everything that happened in the game up to that time. Panel game moves sequence in which each All of the players work (known as common rules), such as a game of chess, is an instance of such a game. By contrast, the example of the game to cross the bridge of Section 1 above shows the game of Information incomplete, because the fugitive must choose a bridge to cross without knowing the bridge Chaser chose to wait, and Chaser makes her Similarly decision in ignorance of the options from the quarry to them. Since game theory is to work on the economic rationalization because of the actions strategically important to others, it should not surprise you to be told that what agents in the games believed, or fail to believe, and about the actions of each other makes a big difference to the logic of our analysis, as we shall see.

2.3 trees and matrices

It is associated with the difference between perfect games and incomplete information to (although certainly not identical with!) To distinguish between the  methods of representation of  the games that are based on the system of play. Let’s start by distinguishing between sequential and simultaneous move games to move in terms of information. It is natural, and the first approximation, to think in sequential step as those games in which players choose their strategies, one by one, and the games one at a time, move as those in which players choose their strategies at the same time. This is not entirely true, however, because what is of strategic importance is not chronological  order  of events per se, but whether and when the players  know about the  other players procedures “in relation to the need of their own choosing. For example, if two companies competing both planning and marketing campaigns, one can commit months of its strategy before the other does not. But if you do not know what some people committed to or will adhere to when making their decisions, and this is the game at one time, move. chess, by contrast, usually played as a game sequential step: see what he had done your opponent before choosing your next work. (Chess  can  be transformed into a game at a time to move if the players all moves call for a joint panel while isolated from each other, but this is a different game completely from the traditional game of chess)

The above has been said that the distinction between sequential move games at one time-step is not identical to the distinction between the ideal information and incomplete information games. Explaining the reason for this is a good way to establish a full understanding of both sets of concepts. Games also marked at one time, a step in the preceding paragraph, it must be true that all the games one at a time, step is to games of imperfect information. However, some games blends sequential and simultaneous movements may contain. For example, two companies marketing strategies independently and may adhere to the confidentiality of each other, but then to engage in price competition in full view of each other. If the optimal marketing strategies partly or wholly dependent on what was expected to happen in the game Pricing later, then you will need to be in two phases to be analyzed as a single game, and that came stage of the sequential play stage of playing at one time. Full games involving the different stages of this type are games of incomplete information, however, has temporarily as it may be. Games full information (as the name implies) indicate the cases in which  no  moves at one time (and where there is no player ever forget what has gone before).

As previously mentioned, games complete information is (logically) the simplest types of games. This is because in such games (as long as the games are limited, that is, after ending unknown number of procedures) players and analysts can use clear procedures to predict the results. A player in such a game chooses her first work by looking at each series of responses and counter-responses that would result from all the action open to it. They then ask himself any of the final results available brings her the highest interest, and choose the work that begins with a series leading to this result. This process is called  incitement back  (because the logic works backwards from the final results to display choice) problems.

There will be much more to be said about the induction back and its properties in the later part (when we come to discuss the balance and equilibrium selection). Now, it has been described only so that we can use to offer one of the two types of mathematical objects used to represent the Games:  trees game. The game tree is an example of what he calls the mathematicians on the  graph-oriented. That is, it is a set of nodes that are related to the overall graph has a direction. We can draw trees from top to bottom of the page, or from left to right. In the first case, the contract is interpreted in the top of the page as it comes earlier in the series of actions. If there is drawn from left to right tree, and the contract is the former left-wing in the sequence of that right. Tree not afford to have a structure of the following type signs:
Figure 1

Games represent a point using trees it could be better grasped by visualizing for use in support thinking backwards induction. Just imagine the player (or analyst) as of the end of the tree, where the results are displayed, and then work backwards from this, looking for groups of strategies that describe the paths leading to it. Since utility player function results indicate that she would prefer that, we also know that she would prefer tracks. Of course, not all trails be possible because the other player has a role in the selection of tracks too, and will not take actions that lead to less preferred his results. We will provide some examples of this interactive path selection, detailed and techniques to think through these examples, after we have described the case we can use the model tree.

The trees are used to represent  consecutive  games, as they appear in the order in which the action by the players. However, the actress games sometimes  arrays  instead of the trees. This is the second type of the object used to represent the sports games. Matrices, unlike trees, appear simply represented in terms of utility functions Results players, each possible combination of strategies may be used to the players. For example, it makes sense to display the game to cross the river from the  Section 1  on the matrix, because in that match all of the fugitive and the hunter is just one step each, and each chooses their move in ignorance of what some have decided to act. Here, then, is  part of the  matrix:
Figure 2

Fugitive three possible strategies across the bridge on the safe, risk on the rocks, or cobra-risk form in the ranks of the matrix. Similarly, three possible strategies hunter waiting on the bridge safe, and wait to rock the bridge and wait Cobra bridge in the form of matrix columns. Each cell of the matrix cells show, or rather  to  show whether the matrix We have a full-on results  specific in terms of players bonuses. Player Award is simply allocated to it by the ordinal utility function of the state of affairs of the results of the corresponding figure in question. Each result, grade reward is always listed first, followed by the column. Thus, for example, the upper-left corner above shows that, when it crosses the fugitive in a safe bridge and the hunter is waiting there, fugitive receive a bonus of 0, and the hunter gets the reward 1. We interpret this reference to the relevant utility players job two “, which in this game is very simple. If you get the fugitive safely across the river it gets a bonus of 1; if you did not get a 0. If you do not Fugitive make it, either because he is shot by a hunter or hit a stone or bitten by a cobra, then the hunter gets a bonus of 1 and fugitive receive a bonus 0.

We will brief explanation of the parts of the matrix that has been filled in, and then say why we can not be completed after the rest. Whenever the hunter waiting on the bridge chosen by the fugitive, it is shot fugitive. These results provide carriers bonus (0.1). You can find them in descending diagonally across the matrix above the upper-left corner. Fugitive choose whenever the bridge is safe, but the hunter waits in another, the fugitive gets safely through, resulting in tankers reward (1.0). These results show the two in the second of two cells from the top row. All other cells marked,  for the time being, with question marks. why? The problem here is that if he crossed the run either in a rocky bridge or the bridge cobra, he enters a border factors in this game. In these cases, it takes on some of the risk of getting killed, and thus reward the production of vectors (0.1), and this is independent of anything the hunter does not. We do not have yet enough of the concepts that have been made ​​to be able to show how the representation of these results in terms of facilities and functions, but by the time we finished, and this will provide the key to solve the mystery of our  Section 1.

It is noteworthy games matrix as’ normal form “or the games’ on the strategic form,” games and the trees are referred to as “wide format ‘games. The two types of games are not similar, because the games wide format, contains information about the sequence of play and levels of players information about the game structure that games strategic model does not. In general, it can be a game of strategic form represents any one of several games and a wide format, in the form of strategic game is best thought of as being a  collection  of games and wide format. When the order of play is irrelevant to the outcome of the game, then you should study the strategic form, where it is a complete set you want to know about. where the system of play  is  relevant, and wide format must  be specific or own conclusions and be unreliable.

2.4 prisoner’s dilemma as an example of the strategic-model versus large-scale, model representation

The differences mentioned above it is difficult to fully understand if all one has to go to a description of the abstract. They are best illustrated by an example. For this purpose, we will use the most famous in all the games: the prisoner’s dilemma. In fact gives the logic of the problem faced by the soldiers of Cortez and Henry V (see Section 1 above), and by agents before Hobbs enable tyrant. However, for reasons it will become clearer later some thing, and you should not take PD as a typical  game. This is not so. We use as an example here only expanded because it is particularly useful to clarify  the relationship  between strategic shape and games and large-format (and later, to clarify the relations between one shot and repeated games; see  Section 4  below).

Derives game of prisoner’s dilemma following the situation usually is used to reflect that name. Suppose that police arrested two people whom they know they have committed an armed robbery together process. Unfortunately, it lacks enough acceptable for the jury to condemn evidence. They  do, but have sufficient evidence to send each prisoner away for two years to steal a getaway car. Chief Inspector now makes the following display for each prisoner: If you confess to the robbery, the involvement of your partner, and it does not also admit that, then you have to go free, she will you get ten years. If you both confess, you get every 5 years. If neither one of you recognize, then you get every two years for car theft.

Our first step in modeling the two prisoners’ status as a game is to represent it in terms of utility functions. Following the usual convention, let’s naming prisoners player I “and” player II. Each of player I am and functions with ordinal utility player for the second identical:

Go for free »4

2 years »3

5 years »2

10 years »0

Numbers are used in a job over now to express each player  bribes  in various possible outcomes in the case. We can represent a problem faced by each of them on a single matrix that captures the way in which separate their choices interact. This is a strategic form of the game:
Figure 3

Each cell of the matrix cells give bribes to both players for each set of procedures. It seems to reward the player I as the first number of each pair, is the second player II. Therefore, if both players admitted afterwards each get a bonus of 2 (5 years in prison each). This appears in the upper-left cell. If neither of them recognize, each get a bonus of 3 (2 years in prison each). This appears as the lower-left cell. If player I recognized the second player then the player does not I receive a bonus of 4 (go for free) and the player gets a reward II 0 (ten years in prison). This appears in the upper-left cell. The reverse situation, in which the player admits II player I refuse, appears in the lower-left cell.

Each player evaluates his or her two actions that can be taken here by comparing the personal bribes in each column, because this shows you any of their business is the best, just for themselves, for each possible action by their partners. Therefore, we note: If the player admitted the second player then I receive a bonus of 2 by recognizing and rewarding of refusing to 0. If he refuses Player II, then the player I receive a bonus of 4 by his own admission and by refusing to reward of 3. So, I player is better off to recognize no matter what you do to player II. Player II, at the same time, evaluate their actions by comparing bribes her down each row, and they come exactly the same conclusion that the player and I do not. Wherever the work of one player is superior to other actions for each action that can be taken by the opponent, and we say that the first act  is dominated by precisely  one second. In PD, then confessing thoroughly dominated refusal for both players. Both players know it from each other, thus eliminating completely any temptation to depart from the path controlled by accurately. Thus, each of the players will admit, and both will go to prison for 5 years.

Players, analysts, can be expected this result using a mechanical procedure, known as the judiciary is dominated by iterative strategies carefully. Player 1 can be seen by examining the matrix bribes to him in every cell of the top row higher than the return on his opposite in every cell of the bottom row. Thus, it can never be between utility maximization for him to play his strategy down the row, which, refusing to recognize,  no matter what you do to player II. Since the strategic bottom row player I will never be played, we can simply  delete  the bottom row of the matrix. Now it is clear that the player and the second does not refuse to recognize, since her return from the recognition of the two cells that remain higher than the return of her refusal. So, again, we can not delete a single cell on the right column of the game. We now have only the remaining one cell, which corresponds to the results arising from the mutual recognition. Since the logic that led us to delete all other possible outcomes stops at each step only on the basis that both players economically rational – that is, the choice of strategies that lead to returns higher on the strategies that lead to the reduction of those, there are strong reasons to watch the joint recognition as  a solution  for the game , the result of which her ​​toys  must  converge to the extent that economic rationality correctly models the behavior of the players. It should be noted that the order in which they are deleted rows and columns is controlled strictly it does not matter. We had begun to delete the right-hand column and then delete the bottom row, we would have arrived at the same solution.

It’s been said a few times that the PD is not a typical game in many respects. One of these aspects is that all the rows and columns controlled by either accurately or thoroughly dominant. In any form strategic game, where this is true, and ensures the elimination of repeated strategies dominated by accurately to yield a unique solution. Later, however, we will see that many of the games do not apply to this condition, and then analytical task we have is less obvious.

Perhaps the reader would have noticed something disturbing about the results of PD. Both players have refused to recognize, and they had arrived at the lower right results which all goes to prison for two years only, and thus both  earn the highest interest of which has both when he confessed. This is the most important fact about PD, and its importance for the theory of the game is very general. But we will return to below when we discuss the concepts of equilibrium in game theory. Now, however, let’s stay with our use of this special game to illustrate the difference between a wide-ranging strategic forms.

When people introduce PD in popular discussions, one often hear them say that the police inspector must lock its prisoners in separate rooms so that they can not communicate with each other. The reasons behind this idea seems clear: if the players may communicate, they want to see certainly they’re all better off if all of refuse, and can make an agreement to do so, is not it? This, one assumes, would remove the conviction of each player that he or she must admit that it will otherwise be sold up the river by their partners. In fact, but this intuition is misleading and the end is not true.

When we represent PD as a strategic form game, and we implicitly assume that the prisoners can not try to agree collusion as they choose their actions simultaneously. In this case, an agreement before the fact can not help. If the player I am convinced that his partner will stick to the deal then he can seize the opportunity to escape away with his own admission. Of course, we realize that the same will happen to the temptation player II; but in this case once again wants to make sure he admits, and this is his only way to avoid the worst result. The prisoners’ agreement to something because they have no way to implement it. Their promises to each other and form what he calls a game theorists “cheap talk”.

But now suppose that the prisoners did  not  move at one time. That is, to assume that the player can choose II after  monitoring the player I work for. This is the kind of situation that the people who think not important communications must be taken into account. Now II player will be able to see the player I remained steadfast when it comes to choice, and they do not need to be concerned about being deceived. But this does not change anything, and this is a point that it is better made ​​by re-representing the game in wide format. This gives us an opportunity pleasure to introduce the game and the way trees appropriate analysis to them.

First, however, here are definitions of some of the concepts that would be useful in a game tree analysis:

Node: the point at which the player chooses action.

Node aid: the point at which the first procedure in the game happen.

Node peripheral: any node which, if reached, the game ends. Each station node corresponds to the result.

Subgame: any set of connected nodes and branches descending unique from one node.

Bonus: utility ordinal number assigned to a player in the outcome.

Result: waiver of a set of rewards, one for each player in the game.

Strategy: Player program instructions which action to take in each node in the tree where they can perhaps be called on to make a choice.

This is a quick definitions may not mean very much to you until you follow them that have been developed for use in our analysis trees below. It is likely to be better if you go back and forth between the two examples and we are working through it. By the time we understand each example, you will find a natural and intuitive concepts and definitions.

To make this exercise useful to the fullest extent possible, let’s assume that the first and second players have studied the matrix above, and they see they’re both better off in represented in the lower-left cell results, have formed a cooperation agreement. I player is a commitment to reject first, and then they will reciprocate the second player when the police ask her to choose. And we will refer to preserve the agreed strategy as a “co-operation”, and will signify in the tree below with ‘C’. And we will refer to the exit strategy of the agreement as a “split” and will denote the tree below with the ‘D’. Each Node 1, 2.3 numbering, …, from top to bottom, for ease of reference in the debate. Here, then, is the tree:
Figure 4

First look at each of the terminal nodes (those along the bottom). These represent possible results. Each is identified with the waiver of bonuses, as is the case in the form of strategic game, with a bonus in the first the first player to appear in each group and the second player to appear II. All structures of the contract descending 1, 2 and 3 is respectively for subgame. We start our analysis using previous versions induction technique called Zermelo algorithm in -With sub-games that arise in the last series of the game. If you play subgame descending from the node 3, then player II will face a choice between a bonus of 4 and a bonus of 3. (See the second issue, which represents a reward, in each group on the descending leg of the node 3. Node) II earns her the highest return By playing D. So we may replace the entire subgame with waiver of reward (0.4) directly to the node 3, since this is the result that will be realized if the game reaches that node. Now consider subgame descending from node 2. Here, II faced with a choice between a bonus of 2 and one of 0. She gets her highest yields 0.2, by playing D. So we may waive the bonus (2.2) directly to the node 2 . Now we turn to the subgame descending from a node 1. (subgame This is, of course, identical to the whole game; all the games are subgames of themselves) player I now face a choice between results (2.2) and (0.4). Consultation with the first numbers in each of these groups, he sees that he gets his highest reward-2-by-play D. D is, of course, recognition of the option. So I recognize the player, then the player also admits II, resulting in the same result as in the representation of the strategic model.

What happened here intuitively is that the player I realize that if he plays C (refusal to recognize) in Node 1, and then player II will be able to maximize the benefit to her by suckering him and play D. (in a tree, and this is happening in the node 3.) This leaves the player with bonus I 0 (ten years in prison), that could have been avoided only by playing D to begin with. Therefore defects of the agreement.

Thus we have seen that in the case of the prisoner’s dilemma, simultaneous and sequential versions lead to the same result. This is often not be true of other games, however. Moreover, it can be resolved only limited large-format (consecutive) games complete information using Zermelo’s algorithm.

As previously noted in this section, and sometimes must represent moves at one time  within the  games that are sequential otherwise. (In all these cases, the game as a whole be one of the missing information, so we will not be able to solve using Zermelo) algorithm. We represent such games using a device of the  devices information. Consider the following tree:
Figure 5

Oval drawn around the nodes  b  and c  indicate that they fall within the group shared information. This means that in this decade Players can not infer a backup track of where they come from. Player II does not know, in the choice of strategy to it, whether in the  b  or c. (For this reason, carry correct numbers in the wide format games are collections of information, portrayed as “action points, instead of the nodes themselves, and this is the reason described the contract within the oval with letters instead of numbers.) In other words, the player II, when selection, does not know what he had done for the player I am in a knot and. But you remember earlier in this section that this is what is known as two of the moves at the same time. So we can see that the method of representation games and trees is a full year. If there is no knot after the initial node is only the information contained on the tree, so that the game has subgame only one (himself), then in the whole game is one of the play at one time. If one node at least share its information with another group, while others alone, the game involves playing both in single and consecutive time, and so is still a game of imperfect information. unless inhabited All information collections through only one node Do we have a game of perfect information.

2.5 solution concepts and poise

In the prisoner’s dilemma, we have represented the results of (2.2), referring to the mutual defection, and was said to be a “solution” to the game. After the economy in general practice and game theorists suggest solutions to the games  and balances.  Philosophically minded readers wanted to ask a question here conceptual: What is the ‘calibrated’ some results game like we are motivated to call them ‘solutions’? When we say that a physical system in equilibrium, we mean that in  the stability of  the state, one in which all internal causal forces balance each other’s system and thus leave it “at rest” until and unless the chaotic intervention of some external factors (ie, ‘foreign’ ) force. This is what economists would normally mean to talk about “balance”. They read economic systems as networks restricts each other (often causal) relations, just like physical systems, and the balance of these systems, then, are stable natural evolution of their states. (Note that in both the physical and economic systems and natural development of stable states may not be observed directly because the systems in an isolated issue never from external influences that drive and destabilize them. In both classical mechanics and the economy, and the concepts of balance are the  tools for analysis, not predictions of what we expect to observe .) As we shall see in subsequent sections, it is possible to keep this understanding of the balances in the case of game theory. However, as noted in Section 2.1, some people explain game theory as an explanatory theory of strategic thinking. For them, it must be a solution to the game, a result that rational agent to predict  using rational calculation mechanisms alone. These theorists encounter some puzzles about the concepts of the solution that are less important to the theorist who does not try to use game theory to what without writing a general analysis of the rational. It is more often the motivation behind the attention of philosophers in game theory through this ambitious than that of non-economists or another world.

It’s useful to start the discussion here of the case of the prisoner’s dilemma because it is simple unusual from the standpoint of the puzzles about the concepts of the solution. What we have referred to as the “solution” is a unique  Nash equilibrium  of the game. (And “Nash” here refers to John Nash, the world of Nobel Prize-winning mathematician who in  Nash (1950)  did most of the expansion and dissemination of von Neumann and Morgenstern in the pioneering work.) Nash equilibrium (from now on “NE ‘) applies (or application failure , as the case may be) for the entire  groups  of strategies, one for each player in the game. There are a range of strategies is the NE only in the event of any player can improve its payoff, given the strategies of all the other players in the game, by changing its strategy. Notice how closely linked to this idea is linked to the idea of a strict dominance: can not be NE strategy strategy if dominated by accurately. Therefore, if the frequency of eradication strategies dominated by carefully takes us to a unique result of their kind, and we know that tankers strategies that lead to this is the NE unique of its kind in the game. Now, almost all theorists agree that avoidance strategies dominated by accurately is  the minimum  rationality and economic requirements. A player who chooses science strategy controlled by accurately directly violates item (iii) of the definition of economic agency as set out in  Section 2.2 . This means that  if  a game has a result that is unique of its kind NE, as in the case of a common recognition in the PD, it must be unique solution. This is one of the most important aspects of PD, which is a game of ‘easy’ (and abnormal).

We can select one category of games that NE is always necessary, but  enough  as a concept solution. This is the perfect game to the limited information which is also the  sum of zero. There is a zero-sum game (in the case of a game involving two players only) one is in any player and only one can be made ​​better off by the other player worse off. (Tic Tac Toe is a simple example of such a game: any move which brings one player closer to victory brings rival closer to the loss, and vice versa) we can determine whether the game is a zero-sum by checking the players’ utility functions: In this zero-sum game will be mirror images of each other, with the results of one player ranked high, which is low in rank to others and vice versa. In such a game, and if I play like that strategy, given your strategy, I can not do any better, and if you  also  to play such a strategy, then, because any change in strategy for me to make you worse off, and vice versa , it follows that our game can be any solution compatible with our mutual economic rationality NE is unique. We can put this another way: in a zero sum ​​game, my strategy, which increases the minimum bonus play if you play the best you can, and its at one time the same thing, it is only  the equivalent of  our play all of the best strategies we have, so this guarantee The pair of so-called action “Top common denominator ‘to find a unique game solution, a unique NE of its kind. (In Tic Tac Toe, this is a tie. You can not do any better than the fee, and I can not, if both of us are trying to win and trying not to losing it.)

However, most games do not have this property. It will not be possible, in this article one, enumerate  all  the ways in which games can be a problem from the viewpoint of possible solutions. (For one thing, it is very unlikely that the theorists and after the discovery of all the potential problems.) However, we can try a little mainstream issues.

First, there is a problem in most of the matches is zero, there is more than one NE, but it does not seem reasonable to all NE on an equal footing with solutions that are reliable players in the case of a strategic strike alert. Consideration in the form of strategic game below (taken from  Kreps (1990), p. 403):
Figure 6

This game has two NE: S1-T1 and T2 S2-. (Note that no rows or columns controlled strictly here but if player I play S1 can then player II do any better than T1, and vice versa .. Similarly the pair S2-T2) if NE is our only solution concept, then we will have to to say that any of these results is convincing on par with the solution. However, if the game was considered as a theory of explanatory theory and / or the standard of strategic thinking, and this seems to be nothing left: certainly reasonable to players with full information to converge on the S1-T1? (Note that this  is not  like the situation in PD, where the situation is socially superior is not feasible because it is not NE. In the case of the above game, both players have every reason to try to converge on the NE for which they are better off.)

This illustrates the fact that NE is relatively (logically)  weak  concept of the solution, often failing to predict reasonable solutions intuitively, because if applied alone, it refuses to allow players to use the principles of selection balance that, if not  demanded  by the economic rationality or the concept of the philosopher more ambitious than rationality, at least it seems both reasonable and can be reached mathematically. Look at another example of the  Kreps (1990), p. 397:
Figure 7

Here, another strategy strictly controlled No. However, top grade player and I S1,  weak  dominated S2, because I do not  at least as well as  the use of S1 S2 as any response from the second player, and respond one by the second (T2), and I’m not the best. You should not therefore players (analyst) delete the row S2 dominated weak? When they do that, then are thoroughly dominated T1 column, it is determined NE S1-T2 is a unique solution of its kind. However, as Kreps goes to show the use of this example, the idea that dominated a weak strategies should be deleted just like those strict consequences odd.  Suppose that  we change the bribes of the game a little bit, as follows:
Figure 8

Still dominate S2 weak as before. But we have two NE, S2-T1 is now more attractive to both players. Why eliminate the possibility of an analyst? (Note that this game, and once again, there  is not a repetition of the logic of PD. There are, it makes sense to eliminate more attractive results, the joint refusal to recognize, because both players have incentives to deviate from one side of it, so it is not NE. This is not true of S2 -T1 in the current game. you should be beginning to see clearly why we call it a game PD “abnormal”.) The argument    for the elimination of strategies dominated weak is that player 1 may be nervous, fearing that player II is not quite sure to be rational economic terms (or that player II fears that the player and I’m not completely reliable logical economic sense, or that player II fears that the player I fear that player II is not completely reliable logical in economic terms, and so on endlessly) and thus may play T2 with some positive possibilities. If you did not take the possibility of going out for a reliable economic rationality seriously, then we have an argument to eliminate the weak strategies dominated: player than I believe in themselves against the worst result, S2-T2. Of course, she would pay for the insurance, reducing yields have expected from 10 to 5. On the other hand, we may imagine that the players can communicate before playing the game and agree to play interrelated strategies  so as  to coordinate  the S2- T1, thus removing some, Most or all of the doubts that encourage the elimination of S1 grade is dominated by weak, and the elimination of S1-T2 as a viable solution instead!

The proposed principle to resolve any games that may have an impact NE eliminate one or more of the solutions to be considered and referred to as  fine-tuning  of the NE. Only in the case discussed, and the elimination of weak dominated strategies is one of the refinement possible, because it refines away NE S2-T1, and the link is the last, because it refines away NE others, S1-T2, instead. So that fine-tuning is more suitable as a concept solution? People who believe in game theory as an explanatory theory and / or normative rationality strategy has generated a large literature is a discussion of the advantages and disadvantages of a large number of improvements. In principle, there seems to be no restrictions on the number of improvements that could be considered, because there may also be no restrictions on a range of philosophical intuitions about what principles agent rational may or may not see fit to follow up or to fear or hope that other players follow .

We now digress briefly to make a point about terminology. In previous editions of this article, we referred to theorists who adopt an interpretation of revealed preference of utility functions in game theory as the “behaviorists”. It reflected the fact revealed preference options equality consistent with the approach of economic measures, rather than intended to refer to the mental structures. However, it is likely to lead to confusion this use because of the recent rise of behavioral game theory  (Camerer 2003). This program aims to integrate research directly to the game generalizations theoretical models, derived mainly from experiments with people, about the ways in which people adopted different from economic factors in the conclusions that we draw from the information (‘formulation’). Applications also usually include assumptions about utility functions, as derived from the experiences. For example, players can be taken to be ready to make trade-offs between the amounts of their own bonuses and inequality in the distribution of bonuses among the players. And we will move on to some of the discussions of behavioral game theory in  Section 8.1,  Section 8.2 and Section 8.3. At present, he noted that this use of game theory crucially depends on assumptions about the mental representation of the value is believed to be common among the people. Thus it will be misleading to refer to behavioral game theory as a “behavioral.” But then only invite confusion to continue referring to the traditional economic game theory, which depends on the preference revealed that she “behavioral” game theory. So will we turn to describing it as “psychological” game theory. I mean by this type of game theory used by most economists who are not Behavioral economists. Game theory are treated as abstract mathematics of strategic interaction, rather than an attempt to characterize the direct psychological own actions that may be typical in humans.

Game theorists is psychological tend to take a dim view of many of the program refinement. This is for the obvious reason that it depends on intuition about the inferences that people  must  find reasonable. Like most scientists, theorists game is suspicious of psychological strength and philosophical basis of assumptions guides the experimental and mathematical modeling.

Behavioral game theory, by contrast, can be understood as a refinement of the theory of the game, but not necessarily of the concepts solve it, in a different sense. It restricts axioms in the basic theory to apply to a special category of agents, and individuals, typical and humans psychologically. It motivates this restriction by reference to the conclusions, along with preferences, that people  do not  find    natural, regardless of whether these seem rational, and this is what you do not so much. However psychological and behavioral game theory involved in it is not intended to be a standard , although all are often used in an attempt  to describe the prevailing standards in the groups of players, as well as  to explain  why the standards may continue to groups of players even when they seem to be less than fully rational philosophical intuition. Whoever sees the function of an applied  game theory as to predict the results of experimental games  because of  the distribution of some of the strategic actions, and the distribution of some expectations about the other strategic actions, which are formed by dynamic players environments, including institutional pressures and structures and choose the evolutionary from. Let us therefore set theorists is psychological and behavioral game together, only for the purposes of contrast to the standard game theorists,  descriptive  theorists game.

Game theorists descriptive often tend to doubt that the aim of seeking a  general  theory of rational logical project. Institutions and processes of evolutionary construction of many environments, and what matters rational procedure as in one environment may not be the favorite in another country. On the other hand, an entity which is not less randomly (ie possibly noisy but statistically more often than not) meet the minimum economic rationality can not be restricted only by accident, and accurately described as designed to maximize function tool. These entities game theory has no application in the first place.

This does not mean that game theorists is psychological abandon its principled ways to restrict groups of NE into sub-groups based on the relative likelihood of emerging access. In particular, theorists game is psychological tend to be sympathetic to the approach that shift the focus from the media on the rationality of the dynamics of games considerations. Perhaps we should not be surprised that NE analysis alone often fails to tell us a lot of application, experimental games strategic interest for the model (for example, Figure 6 above), which are suppressed informational structure. And often address issues choose a more productive balance in the context of large-format games.

2.6 perfect Subgame

In order to deepen our understanding of the games wide format, and we need a more exciting example with the structure of interesting offers from PD.

Look at the game, which he described this tree:
Figure 9

It is not intended to fit this game with any prior condition. It is simply a mathematical object in search of the application. (L and R here only “left” and “right” denote respectively.)

Now consider the strategic shape of this game:
Figure 10

If you’re puzzled by this, remember that the strategy must say the player what to do in  all the information received since the player has work. Because each player chooses between two actions on each of the two sets of information here, each player has four strategies in total. The first character in each label strategy tells every player what to do if he or she reaches the first set of their own information, and second what to do if it is to reach a second set of their information. LR any player II II says to play L if the information contained 5 is reached and R if you put the information that reached 6.

If you are studying the matrix in Figure 10, you will discover that (LL, RL) is among the NE. This is a puzzling thing, because if the player second information I have got a group (7) in the game wide format, she hardly want to play L there. Earn higher returns by playing in a knot R 7. NE analysis just do not notice this because the NE is insensitive to what is happening  off the road from the play. The first player, in the selection of L in the node 4, ensures that the node 7 will not be reached; this is what is meant by saying that “the way off from playing.” In the analysis of matches and wide format, but we  must  care about what happens off the road to play, because the consideration of this is crucial to what happens  on the  track. For example, is the fact that the player and I  will play R if a node 7 was reached  that  caused player II to play L if reached to a node 6, and this is why a player I will not choose R in a knot 4. We throw away the relevant information for the game Solutions if we ignore the results out of the way, as it does just NE analysis. Note that this is reason to doubt that the NE is the concept of balance entirely satisfactory in itself has nothing to do with intuition for rationality, as is the case for fine-tuning the concepts discussed in Section 2.5 something.

Now apply Zermelo algorithm on a broad form of current for example. We start again with the last subgame, which descend from the node 7. This is to move the player I am, and it will choose R because they prefer to have a yield of 5 to reward of 4 she gets by playing L. Therefore, we set payoff (5, – 1) to the node 7. Thus in knots 6 II faced with a choice between (-1.0) and (5, -1). L. chosen in knots 5 II picks in R. 4 I node and then choose between (0.5) and (-1.0), and so plays L. Note that, as is the case in PD, this result is shown in node – station (4.5) of the 7-knot that Pareto superior to the NE. Once again, however, and the dynamics of the game prevented him from reached.

The fact that Zermelo algorithm to choose a strategy tankers (LR, RL) a unique solution of its kind of game shows that the return of something other than just NE. In fact, it works to create a game  subgame perfect equilibrium  (SPE). He gives a result which gives NE not only in the entire  game, but every subgame as well. This is the concept of a convincing solution to that, again unlike the improvements section 2.5, it does not call for the “extra” rational agents in the sense you expect them to have and use intuition philosophical about “what makes sense. It does, however, assume that the players know everything relevant strategic to their situation, but also  the use of  all that information. In the debate about the foundations of the economy, and are often referred to this aspect of rationality, as in the phrase “rational expectations”. However, as noted earlier, it is best to be careful not to confuse the general standard of rationality with the idea of computational power and possession of budgets, in time and energy, to achieve the maximum benefit from it.

Agent play subgame perfect strategy simply choose, in each arrival node, and the path that brings her the highest payoff  in subgame emanating from that node. SPE expects a match, and just in case, in the resolution of the game, and the players expect that they will do all that.

A key value for the analysis of matches and wide format for SPE is that this can help us to identify the structural barriers to social improvement. In the current example we have, the better off I’ll be operator, the operator II is not worse off, in the left-hand knot-ups from 7 knots him on the results of SPE. But economic rationality player I am in the second and awareness of this player, and blocks socially effective results. If our players want to achieve more socially efficient outcome (4.5) here, you must do so by re-designing their institutions in order to change the structure of the game. Enterprise change institutional and information structures so as to make effective results probably in the games that agents (that is, people, businesses and governments, and so on) in fact play is known as  the design of the mechanism, which is one of the pioneers in the application of game theory areas. The auditing of key technologies in  Horowitz and Reiter (2006), the first author who won the Nobel Prize for pioneering work in the region.

2.7 Payments explanation: ethics and efficiency in Games

Many readers, but especially philosophers, you may wonder why, in the case of example addressed in the previous section, and should be a mechanism design necessary unless the players puny selfish sociopaths. It is certain that the players may be able to just  see  this result (4.5) socially and morally. And because the whole issue also takes for granted that could also see the path of actions that lead to the effective result of this, is the scene of the game to announce that it has not changed the game, and it’s unattainable? This objection, which applies to the distinctive idea of rationality urged by Immanuel Kant, shows on the road when many philosophers means more than before “rationality” of descriptive game theorists do. Is to explore this topic with great vitality and strength of the dialectic in Binmore (1994, 1998).

This weighty philosophical debate about rationality and confused sometimes a misunderstanding of the meaning of “benefit” in the game is the psychological theory. To eliminate this error, look at the prisoner’s dilemma again. We have seen that in a unique NE of PD, both players get less useful than they could be through mutual cooperation. This may strike you, even if you do not Kant (Hit as many commentators) as harmful. Sure, it might think, it is simply the result of a combination of selfishness and paranoia on the part of the players. To begin with they have no regard for social interest, and then shoot themselves in the foot by being untrustworthy also to respect the agreements.

This way of thinking is very common in popular discussions, and mixed severely. To dispel its influence, let us first introduce some terminology to talk about the results. Economists usually measure the care of social good in terms of  efficiency Barreto. It is said that the benefit of β distribution to be Pareto superior  to δ another distribution only in the case of the state of δ there redistribute the possible benefit for beta such as the player and at least one is better off in the β than in the δ and any player is worse off. The failure to move from the lowest to the Pareto distribution Pareto superior is  ineffective  because of the presence of β as a possibility, at least in principle, showing that δ is wasted in some facilities. Now, the result (3.3), which represents mutual cooperation in our model of PD clearly Pareto superior to mutual defection. In (3.3)  both  players are better off than they were in the (2,2). So it is true that the party lead to ineffective results obtained. This example of our applies in Section 2.6 as well.

However, it should not be associated with inefficiency debauchery. It is assumed that the player utility function to represent  everything that a player cares, and that anything that might be at all. As we have described the situation of our prisoners they do in fact only care about special relativity in prison, but there is nothing essential in this area. What makes a game PD unparalleled precision and her only reward structure. Thus, we can have two types of Mother Teresa here, both of which do not pay much attention to themselves and wish only to feed hungry children. But suppose the original Mother Teresa would like to feed the children in Calcutta while the mother Juanita wants to feed the children in Bogota. We assume that international aid agency will double the donation if the two run the same city of the saints, and will give the second-highest amount if the naming cities each other, and the lowest amount if all the nomination of their city. Saints we are here in the PD, although almost selfish or indifferent to the social good.

Go to our prisoners, to assume that, contrary to our assumptions, they  do  value each other’s well-being as well as their own. In this case, and this must be reflected in the functions of their usefulness, and therefore in receiving their bribes. If the change is flawed structures, so that, for example, they are very bad about contributing to the inefficiency feel that they prefer to spend additional years in prison endure shame, then they will not be in the PD. But all this shows that not every possible case is PD. It  does not  show that selfishness are among the assumptions of game theory. This is the  logic of the  prisoners’ situation, and do not have a psychology, to make them suffer in the non-effective results, and if this really  is the  situation then they find themselves trapped in it (to prevent further complications which will be discussed below). Agents who want to avoid the results are effective best advised to prevent some of the games from emerging. Defender of the possibility of rationality Kant is really suggests they try to dig themselves out of such games by transforming themselves into different types of agents.

In general, then, it is partly a game  defined  by allocated to the players bonuses. In any application, and these assignments should be based on sound empirical evidence. If the proposed solution involves an implicit change of these positives, this “solution” is in fact a convincing way to change the subject and avoid the effects of the best modeling practices.

2.8 trembling hands and quantitative response poise

We have another point above opens the way to a philosophical puzzle, one of several that still operates concerned rationales to the theory of the game. And it can be raised with respect to any number of examples, but we will borrow one of the elegant and C. Bicchieri (1993). Consider the following game:
Figure 11

Here are the results of NE in one node descending the far left of the node 8. To see this, Jund back again. In the node 10, and I would like to play L to reward of 3, giving II payoff 1. II can do better than that by playing L in knots 9, giving me a bonus of 0. I can do better than that by playing L in 8 knots; so this is what he does, and the game ending II without getting on the move. Then put the puzzle Bicchieri (along with other authors, including Binmore (1987)  and Petit and Soden (1989)) by the following logic. Player plays IL at the node 8 because they know that player II is a logical economic sense, and it will be in a knot 9, play L Player II knows that the player I am is a logical economic sense and that, in the node 10, and played L. But now we have a paradox the following: the player must assume that player II, in the node 9, the prediction play player I rational economically in the node 10 although arrived to a node (9) which can be reached only if the player and I’m not a logical economic sense! If player and I is not logical in economic terms and then is not justified player II in predicting that would player does not play R in the node 10, and in this case it is not clear that the Player II should not play R 9; and if a player II plays R 9, then the first player guaranteed payoff of better then they get if they play in a knot L 8. Both players use extrapolation backward in order to solve the game. Induction requires that the back of the player and I know that player II player knows that I am not a logical economic sense. But player II can be solved only game using the argument that takes a backward induction hypothesis player I failed to act in accordance with economic rationality. This is the  paradox induction back.

There is a common way to overcome this paradox in literature is to invoke the so-called “trembling hands” because of  Selten (1975). The idea here is that the decision and the reaction to it of the results may “come apart” with some non-zero probability, no matter how small. That is, the player may intend to take action but then stumbled in the execution and send the game down some other way instead. If there is even a remote possibility that the player may make a mistake that have a “hand may tremble’- then be entered no contradiction by the player using the argument incitement underdeveloped that require a hypothetical assumption that another player has taken a path that economically player rational can not choose . In this example, the player can II thinking about what to do in a knot 9 conditional on the assumption that the player chose L in 8 knots but then decline.

Gintis (2009)  suggests that the paradox arises not only from our point of view to assume that both players economically rational. It is based decisively on the additional premise that every player should know, and the reasons on the basis of science, that the other player is economically rational. This is the premise that each player guesses about what might happen off the road balance inconsistent play. A player has reason to consider the possibilities to get out of balance if either believes that its rival is rational economically, but his hand may tremble  or  they are attached to some of the possibilities is a zero to the possibility that it is not rational in economic terms  or  they attached some doubt to believe her about the utility has a function . Gintis also confirms, solving the issue with a broad form of games Games in September by the algorithm in Zermelo circulate: the player does not have a reason to play until the  Nash  equilibrium strategy, she expects other players to also play the Nash equilibrium strategies. We will return to this issue in  Section 7  below.

The paradox of incitement back, such as puzzles raised by the refinement that balance, it is mainly a problem for those who consider the theory of the game also contributes to the standard theory of rationality (specifically, contribute to this theory, the theory of larger  strategic  rationality). Game is psychological theorist can give a different kind of mind appeared to play “irrational”, wisdom and encourage. This involves an appeal to the empirical fact that the actual agents, including people, and we must  learn  balance games strategies that play at least whenever the games at all complicated. Research shows that even a simple game such as the prisoner’s dilemma requires learning by person (Ledyard 1995,  Sally 1995,  Camerer 2003, p. 265). What does it mean to say that people must learn to balance strategies is that we should be a bit more complicated than had been shown in the construction of facilities and functions of behavior in the application of preference theory it revealed earlier. Instead of building utility functions on the basis of one episode, we must do so on the basis of observed behavior runs  once they settled it, which shows the maturity of learning is mentioned, the game in question. Once again, the prisoner’s dilemma makes a good example. Few people facing dilemmas of one shot a prisoner in everyday life, but they face many  frequent  in PD with no strangers. As a result, when put to what is intended to be PD- one shot in the experimental laboratory, people tend to play at first as if they were one game tour of repeated PD. And repeated PD has many Nash equilibria involving cooperation rather than split. Thus, experimental subjects tend to cooperate at first in such circumstances, but after learning some number of rounds on dissent. The experimenter can not conclude that it may be caused by successfully PD- one shot with the experimental setup even see this behavior stability.

If players are aware of the games that other players may need to know the game structures and balances of experience, and this gives them a reason to take into account what is happening outside the balance games paths wide format. Of course, if a player is feared that other players have not learned the balance, and this may well remove the incentive for her to play the same balance strategy. This raises a set of deep problems about social learning (Fudenberg and Levine 1998. How players ignorant learn to play balances if advanced players can not show them, because it is stimulated and advanced to play equilibrium strategies even learned ignorant? Decisive answer in the case of game theory applications to the interactions between people is that young people  socially through growing up in networks of    institutions, including the criteria cultural. Most complex games that people already play in progress among the people who were socially by them and that and, we have learned the structures of the game and balances (Ross 2008A. Beginners should only then copy Those who seem to be expected and understood by others play. norms and standards is rich with reminders, including sermons and easily remembered rules of thumb, to help people remember what they are doing (Clark1997).

As noted in  Section 2.7  above, when observed behavior  does not  settle on the balance in the game, and there is no evidence that learning is still in process, the analyst must conclude that it is similar to the situation it was considering incorrectly. Chances are that have either ill-defined benefit players with jobs, and strategies available to the players, or the information available to them. Given the complexity of many cases where he taught social scientists, we should not be surprised that poor models specifications happen often. Should be applied game theorists do a lot of learning, just like their subjects.

Thus, the irony backward induction is only apparent. However, if the players saw playing in balance with each other in the past, even if they are all logical in economic terms and all believe this one from the other, we should expect that it will attach some positive possibilities to think that understanding of the game structures between some of the players is full. This then explains why people, even if they are economically rational agents, may often, or even usually, playing as if they believe in trembling hands.

Learning from balances may take different forms for different representatives and Games levels of complexity and different risks. Include it in game theory models of the interactions and thus offers a new wide range of technologies. General theory most fully develop, and the reader is referred to  Fudenberg and Levine (1998).

The above was said that people might  usually  play as if they believe in trembling hands. The reason for this is that when people interact, the world does not provide them with cue cards and advising them about the games they play structures. We must make and test conjectures about this from the social contexts. Sometimes, the rules are fixed institutional contexts. For example, when a person walks in a retail store and see the price on something she would like to have, and she knows without having to guess or find out anything they participate in the ‘take it or leave it “a simple game. In other markets, she said They may know that they expect to haggle, and find out the rules for that as well.

Because of the complex relationship between unresolved learning theory and game theory, and logic may seem above it means you can not apply this theory to game situations that include human players that are novel to them. Fortunately, however, we face no such dilemma. In a pair of papers affecting the mid-to-late 1990s, McKelvey and Palfrey (1995,    1998) developed the concept of solution equilibrium quantitative response (QRE). QRE not refine NE, in the sense of being philosophically motivated effort to enhance the NE by reference to the standard criteria of rationality. It is, rather, the method for calculating the balance of the options developed by the characteristics of the players who guesses about possible errors in other players choices is uncertain. Thus QRE standard equipment in the toolkit of experimental economists who are trying to estimate the distribution of utility functions in the population of real people put in situations similar to match. QRE will not practicable to serve in this way for the development of packages such as Stata econometric (TM) allows QRE account given a strong enough control of complex games interesting records. And rarely used QRE by behavioral economists, almost never used by psychologists, in the laboratory analysis of the data. As a result, many of the studies by the researchers of these species make dramatic rhetorical points by ‘discovery’ that real people often fail to converge on the NE at trial matches. But NE, although it is the concept of moderate solution in one sense because it strips away from a lot of informational structure, is at the same time expect the trial, demanding if imposed definitive (that is, if it is expected to play as if they’re all sure All other players are playing strategies NE). Expected to play consistent with QRE correspond to reality, it is driven by the view that NE embodies the basic concept for the overall strategic balance. One way to frame the philosophical relationship between the NE and QRE are as follows. NE known  logical  principle which are well adapted to the discipline of thought and visualize new strategies for general models of new categories of social phenomena. For the purposes of estimating real experimental data one must be able to determine the balance statistically. QRE represents one way to do so, consistent with the logic of NE.

3. uncertainty, risk and serial poise

We have similar games to this point have all the players involved to choose from among the  strategies pure, seeking every one of the optimal course of action on each node, which is the best response to the actions of others. Often, however, it has been improved player facilities through the use of  mixed strategy, which was weighted currency fluctuation between several possible actions. (We will see later that there is an alternative explanation for mixing, does not involve randomization in a certain information, but we will start here from the interpretation of flipping a coin and then build on it in Section 3.1.) And the so-called mixing whenever not pure strategy increases the player against all strategies Discount Rate . We have a game to cross the river from Section 1  embodies this. As we have seen, the puzzle in this game lies in the fact that if you choose a certain logic fugitive bridge optimally, it must be assumed Chaser him to be able to repeat this logic. Fugitive can escape unless his pursuer can not be predicted reliably and the bridge that will be used. Similar to the power of logical thinking on the part of two of the players ensures that the fugitive could surprise the pursuer only if it was possible for him to surprise himself.

Suppose we ignore the rocks and cobra for a moment, and imagine that safe bridges alike. Let’s also assume that the fugitive has no particular Chaser him that it might lead to adventure probability distribution intuition to know specifically Chaser available strategies. In this case, the best path is a fugitive roll die three aspects, which represents a different bridge each side (or more traditionally, the hexagonal die that is the representation of each bridge by two sides). You must then commit himself before using any bridge chosen this  device randomizing. This limits the chances of survival regardless of what he does Chaser. But since the Chaser has no reason to favor any pure or mixed strategy available, since in any case we’re assuming cognitive situation it is to be symmetrical to that of the fugitive, we may assume that it will roll the die three aspects of her own. Fugitive now has a 2/3 probability of escape and Chaser 1/3 the possibility of infection. No fugitive pursuer can not improve their chances because of a combination randomizing the other, so a couple of random strategies are in the Nash equilibrium. Note that if  one  is a random player and then on the other hand are well on an equal footing in  any combination of the above possibilities of bridges, so there is an infinite number of combinations of the best responses. However, each player must worry that anything other than a random strategy may be coordinated with some factors other player can detect and exploit. Because any strategy is random is exploited by a strategy other than random, in a zero-sum game, such as our example, but the strategies of random vectors is NE.

Now let’s re-introduction of border agents, that is, and falling rocks on the bridge No. 2 and Cobra in bridge # 3. Again, let’s assume that the fugitive is sure to get safely across the bridge No. 1, has a 90% chance of crossing No. 2 Bridge, and a chance 80 % of crossing the bridge # 3. We can this new game solved if we make some assumptions about the utility functions of the players two. “Let’s assume that player 1, the fugitive, only cares about life or death (preferring life to death) while the Chaser Todd simply to be able to report that the fugitive is dead, and I preferred this to having to report that he managed to escape. (In other words, no player is interested in  how to  live a fugitive or die.) Let’s also assume at the moment that the player any benefit or do not get not benefit from taking more or less risk. In this case, the fugitive simply takes his original randomizing weights formula by different levels of parametric risk in the three bridges. We must think of each bridge as a  lottery  on the potential fugitive results, and that in every lottery has a different  payoff expected  in terms of the elements in the function of accompanying him.

Consideration of the issues from the standpoint of Chaser’s point of view. She will use her NE strategy when choosing a combination of the possibilities on the three bridges that make the fugitive indifferent between his pure possible strategies. Bridge with rocks is 1.1 times more dangerous for him than a safe bridge. Therefore, it will be indifferent between the two when the pursuer is likely to be waiting at the bridge safe from rock bridge 1.1 times. Cobra bridge is 1.2 times more dangerous to runaway from a safe bridge. Therefore, it will be indifferent between these two bridges at the prospect of waiting Chaser when a secure bridge 1.2 times higher likelihood of it on the bridge cobra. Suppose we use S1, S2 and S3 to represent the survival of life fugitive in a border bridge all rates. Then Chaser reduces the survival rate of net life through any pair of bridges by adjusting the P1 and P2 chances are they will wait on them so

S1 (1 – P1) = S2 (1 – P2)

Since P1 + P2 = 1, we can rewrite this as

S1 × P2 = S2 × P1

so

P1 / P2 = S1 / S2.

Thus Chaser find NE her strategy by solving the following simultaneous equations:

1 (1 – P1) = 0.9 (1 – P2)
= 0.8 (1 – P3)

P1 + P2 + P3 = 1.

then

P1 = 49/121
P2 = 41/121
P3 = 31/121

Now let F1, F2, F3 represents the possibilities that the fugitive picks each bridge them. Then find the fugitive NE him by solving strategy

S1 × F1 = S2 × F2
= S3 × F3

so

1 × F1 = 0.9 × F2
= 0.8 × F3

At one time with

F1 + F2 + F3 = 1.

then

F1 = 36/121
F2 = 40/121
F3 = 45/121

These two sets of possibilities NE tells each player how to weigh his or her die before the throw. Note-perhaps-surprising result, fugitive, although by the hypothesis he will not get the enjoyment of gambling, uses a high-risk bridges with  the highest  probability. This is the only way to make Chaser indifferent on the bridge, which was lots of it, which in turn is more than the possibility of fugitive survive.

We were able to solve this game directly because we set the same benefit in such a way as to make it  job-sumzero, or  the competition is strict. That is, all of the increase in the expected benefit by one player is strictly symmetrical loss by the other party. However, this requirement may not be held more often. Now suppose that the utility functions, is more complex. The most preferred Chaser This result, which was firing at the fugitive and that thanks to arrest him to one who died in the rockslide or snakebite. She prefers this second result of his escape. Fugitive prefer a quick death by firing squad for the pain of being crushed or horror encounter with a cobra. Most of all, of course, he would prefer to escape. Suppose, apparently, that the fugitive much care strongly  about surviving than it does about getting killed one way rather than another. We can not solve this game, as it was before, simply on the basis of knowledge of the players ordinal utility functions, because the intensity of preferences, each will now be related strategies.

Before the work of  von Neumann and Morgenstern (1947), and it has been cases of this kind inherently puzzling to analysts. This is because the benefit does not indicate a subtle psychological variable such as pleasure. As we discussed in  Section 2.1, the tool is just a measure of the relative behavior of behavioral given certain assumptions about the consistency of relations between the preferences and choices. And therefore it is illogical to imagine compared to our players, “Cardinal -mn is, sensitive preferences with each other density, as there is no, fixed scale independent interpersonally we can use. How, then, we can play in any key information is relevant? After model everything, and put games models require that the facilities all the players to be taken into account at a time, as we have seen.

There is a very important aspect  von Neumann and Morgenstern in (1947)  and the work of a solution to this problem. Here, we will provide a brief overview of their technique ingenious to build facilities essential functions out of that hierarchy. It was emphasized that what follows is just an  outline, so as to make basic facilities is mysterious to you a student who wants to know about the philosophical foundations of the theory of the game, on a range of problems that can be applied. Provide evidence could follow in  building  facilities and functions Cardinal your many pages requires. Available in many books such evidence.

Suppose that we now have the following ordinal utility function of the fugitive-set cross the river:

Escape »4

Death by shooting »3

Death rockslide »2

Death snakebite »1

We assume that his preference to escape more than  any  form of death is stronger than the preferences among the causes of death. This behavior should be reflected in the choice of the following way. In a game such as crossing the river, and should be ready to run greater risks to increase the relative probability to escape the fire, which is to increase the relative likelihood of fire during the snakebite. This bit of logic is the crucial insight behind  von Neumann and (1947) Morgenstern in the  solution to the problem cardinalization.

Suppose we asked the fugitive to choose from a range of available results, which is  the best  one  and the worstone. “Best” and “worst” are defined in terms of bonuses is expected as described in our current zero-sum game, for example: a player maximizes returns expected of him if, when choosing between a lottery that contains only two possible awards, he always picks it maximize the best prospect for a result of this call    W- and reduce the likelihood of the worst-call results of this L. Now imagine expand the range of possible awards to include awards, estimated the agent as an intermediate between  W  and L. We find, for a set of results that contain such prizes, the lottery so that our agent is indifferent between the lottery and sweepstakes, including all  W  and L. In our example, this is a lottery, which include fire and crushed rocks. This lottery call T. determine the function of the tool  P  =  u (T) of the results of the real (as opposed to ordinal) line numbers so that if  P  is expected in the prize    T, and the agent is indifferent between winning T  and win the lottery  T *  where  W  is happening with the possibility of  u ( T)   and L  occurs with probability 1 –  u (T). Assuming that the agent behavior that respects the principle of  reducing the lottery compound  (ROCL) -mn is, do not gain or lose the benefit of considering the lottery more complex instead of those, and a simple set of results appointments in  T  u T * gives the von Neumann-Morgenstern utility function (vNMuf) with infrastructure at all results in T.

Exactly what we have done here? We have given our agent options more than a lottery, rather than directly on the results of the resolution, noted the extent of an extra risk of death that he was ready to run to change the odds of getting one form of the death of proportion to an alternative form of death. Note that this is only the agent cardinalizes preference structure for the reference points agent specific  W  and L; procedure reveals nothing about the comparative preferences outside the hierarchy  between the  agents, which helps to clarify that the building does not enter vNMuf psychological element is likely to be objective. Moreover, two of the agents in one game, or one agent under different types of conditions, may expose the varying attitudes to risk. Perhaps in the game to cross the river and the pursuer, his life is not in danger, and enjoyed gambling with her ​​glory while the fugitive is our caution. In game analysis cross the river, but we do not  have to  be able to compare the basic amenities Chaser with fugitive. Each of the agents, after all, can be found NE strategies if they can be appreciated all the possibilities will be allocated to the actions of the other party. This means that all should know all of vNMufs. But do not need to try to assess the comparative results of more than that they choose.

We can now fill in the rest of the Matrix game to cross the bridge, which we started drawing in Section 2. If both players neutral to risk and their preferences revealed respect ROCL, then we have enough information to be able to customize the expected utilities, expressed by multiplying the original bribes of possibilities related, and results in the matrix. Let’s assume that the hunter waiting at the bridge with the potential for Cobra  Q  When a rocky bridge with the possibility of y. Since its possibilities across the three bridges should amount to 1, this means that they must wait at a safe bridge with the possibility of 1 – (x  + y). Then, and continue to set fugitive reward of 0 and 1 if he dies if he escapes, and the fisherman in reverse receive bribes, full matrix we have are as follows:
Figure 12

We can now read the following facts about the game directly from the matrix. No pair of pure strategies is a pair of the best responses to the other. Therefore, the only NE game requires the player and at least one to use a mixed strategy.

3.1 beliefs and self-odds

In each of the examples and work to this point, we have assumed that the players beliefs about the possibilities in the lottery game objective probabilities. But in cases of selecting a truly interactive, agents must often rely on subjective estimates or perceptions of the possibilities. In one of the largest contributions in behavioral and social sciences in the twentieth century,  Savage (1954)  showed how to integrate Resume possibilities, and their relationships to risk preferences, in the von Neumann-Morgenstern expected utility theory framework. In fact, the achievement of Savage reported the formal completion of the EUT. Then, later in just over a decade, Harsanyi (1967)  showed how to solve the games involving the maximum benefit from brutal expected. And often take this and put the real maturity of game theory as a tool to mark applied to the behavioral and social sciences, and recognized as such when it joined Nash, Harsanyi and Selten as the recipient of the first Nobel Prize awarded to game theorists in 1994.

As we noted in considering the need for people to play games to learn trembling hand and balances QRE, when we strategy model the interactions of people and we must allow for the fact that people are not sure of their models usually about each other. This uncertainty is reflected in their choices of strategies. Moreover, some actions can be taken precisely in order to learn about guessing the player for other players accuracy. Harsanyi extension of game theory includes these critical elements.

Consider the three players for the game-down missing information known as the “Selten’s horse” (for its inventor, Nobel Prize Reinhard Selten, and because of the shape of the tree; taken from  Kreps (1990), p. 426):
Figure 13

This game has four NE: (L, to 2, to 3), (L, p. 2, to 3), (R, p. 2, to 3) and (R, p. 2, p. 3). Consideration of the fourth of this NE. He arises because when the player plays IR player II plays p. 2, a full player group III in information is outside the path of play, and it does not matter to the results of what he is doing Player III. But the player I would not play R if Player III can tell the difference between being in 13 knots and being in a knot 14. The structure of the game incentivizes player I’s efforts to provide the player with the III information that would open up closed her information group. III player must believe this information because the game structure shows that the player I have an incentive to inform them honestly. The solution then is the game of SPE (now) is perfect for game information: (L, p. 2, L 3).

Theorists who believe in the theory of the game as part of the standard theory of rational public, for example, most philosophers, and enthusiasts refinement among economists program, has pursued a strategy that will select this solution on general principles. Note what III player in the horse Selten have wondered about his strategy because he chooses. “Given that I get on the move, it was reached practical knots from 11 knots or 12 knots?” What, in other words, are  the possibilities policing  that is the third player in 13 or 14 knots, given that he has step? Now, if the conditional probabilities are wondering what player it III, then the first and second players have made ​​guesses about when they select their  strategies and the third player in  beliefs  about these conditional probabilities. In this case, the player I have to guess about the second player beliefs about beliefs third player in the player and beliefs about beliefs III player-II, and so on. Relevant here beliefs are not just a strategy, as it was before, because it’s not only about what the players will  not  be given a set of rewards and structures of the game, but about understanding the conditional probability that they should expect other players to work with.

What beliefs about the conditional probability Is it possible for the players to expect from each other? If we follow  Savage (1954)  suggest that the normative principle should be that the mind and expect others to the cause, according  to the rule of Bayes and. This tells them how to calculate the probability of occurrence of the event information contained F E (wrote ‘public relations (F / E)’):

Public Relations (F / E) = [PR (E / F) × PR (F)] / PR (E)

If we assume that the players beliefs always be consistent with this equality, we could determine the balanceserially. A SE of two parts: (1) Profile § strategy for each player, as before, and (2) of the  system of beliefs microns for each player. μ assigns to each set of information  h  probability distribution over the decade in    h, with the explanation that these are the beliefs of player i (h) for a place in his information a group that, given the information that a group of  h  had been reached. Then the serial balance is a glimpse of § strategies and system of beliefs microns consistent with the rule of Bayes in like this starting from each set of information  h  in a tree operator  i (h) plays optimally From then on, given that what was believed to have been Previously event given by Μ (h) what will transpire in the subsequent moves are given by §.

Let’s apply this concept to solve Selten’s horse. Consider again in the NE (R, p. 2, p. 3). Let’s assume that player III appointed Public Relations (1) in the belief that if she gets the step is in the node 13. Then the player I, given μ constant (I), must believe that the player III will play for 3, and in this case it just SE strategy L . in spite of that (R, p. 2, to 3) is the NE, it is not SE.

The use of consistency requirement in this example is trivial to some extent, so consider now the second case (also taken from  Kreps (1990), p. 429):
Figure 14

Let’s assume that player plays IL, II player playing for two  player third play for 3. Let’s also assume that μ (II) appoint a public relations (0.3) to a node 16. In this case, for two  not SE player II strategy, since for two  revenue her expected return of 0.3 (4) 0.7 (2) = 2.6, p while 2  brings the expected reward of 3.1. Note that if we fiddle profile strategy III player while leaving everything else constant, for two  can  become  SE player II strategy. If § (III) resulted in a play for 3  with public relations (0.5) and Y 3  with public relations (0.5), then if a player plays the second p 2  to yield the expected him now to be 2.2, so (LP 2 for 3) would be SE. Now imagine setting μ (III) again as it was, but the change μ (II) so that player II believes that the conditional probability being 16 knots greater than 0.5. In this case, for 2  again is not SE strategy.

SE hope the idea is now clear. We can be applied to game cross the river in a way that avoids the need for any pursuer on the face of the coins we adjust the game a little bit. Now suppose that the Chaser bridges can change twice during the passage of the fugitive, and will only catch it if you meet him as he left the bridge. Then SE Chaser’s strategy is to divide her time on the three bridges, according to a certain proportion of the equation in the third paragraph of Article 3 above.

It should be noted that since the Bayes rule can not be applied to events with the potential to be applied to 0 SE requires that players set non-zero probability for all procedures available in wide format. This requirement is captured to suppose that all the features of the strategy are  mixed thoroughly, which means that all the work in each set of information to be taken with a positive prospect. You will see that this is equivalent to just assume that all hands tremble sometimes, or alternatively that there are no very specific expectations. It is said that the SE  trembling hand is ideal  if all the strategies played in the balance is the best responses to the strategies that blend perfectly. Also it should not be surprised to be told that there is no strategy dominated by the weak can be a trembling hand perfect, because the possibility of trembling hands gives players the most convincing reason to avoid such strategies.

How can a game theorist is psychological understanding of the concept of NE this is the balance in all the acts and beliefs? The decades of the pilot study showed that when humans play games, especially games that are ideally calls for the use of Article Baez to make guesses about the beliefs of other players, and we should expect a large  heterogeneity  in strategic responses. Multiple types of media channels usually associated with various factors incentive structures in their environments. Some of the factors that can be calculated in fact balances, with more or less wrong. Others may settle within the ranges of error drift randomly around the equilibrium values ​​by learning more or less myopia conditioned. Still others may select the response by copying the behavior of other factors, or by following the rules of thumb that are embedded in the cultural and institutional structures and represent the historical part of collective learning styles. Note that the issue here is specific to game theory, instead of being a mere repetition of a more general point, could apply to any learned behavior, that people vociferously act from the standpoint of ideal theory. In a particular game, whether it’s even rational, agent Psychology, mathematically resources well trained to play NE will depend on the frequency with which he or she expects others to follow suit. If you were expecting some other players to stray from playing NE, and this may give her a reason to move away itself. Rather than expecting that the human players will reveal strict Near East strategies, and fitter experienced modeler or expected that there would be a relationship between the play and expected costs from out of the NE. As a result, the maximum likelihood estimate of the observed actions usually determines QRE provide better than any NE bout.

It explains the analyst must not deal with the experimental data in this way as the “hypothesis testing” that agents under analysis is “rational.” Instead, they are guessing that they are agents, that there is any systematic relationship between changes in the statistical patterns in their behavior and some Cardinal weighted rankings the potential risks of the target states. If agents persons or organized groups institutionalized people that monitor each other and incentives in an effort to work collectively, and often considered this guesses as reasonable by the critics, or even practical unquestionable, even if it is always due to the lack defeasible zero possibility of mysterious circumstances a strange kind of philosophers consider in some cases (for example, people apparently are mechanical simulacra is smart pre-programmed that it will be revealed as such only if not written responses to the environment and stimulating in their programs). Analyst may assume that each of the agents respond to changes according incentive Savage expected theory to public facilities, particularly if the factors are the companies that we have learned emergency response under conditions demanding standard of competition in the market with many players. If an analyst themes are individual people, especially if they are in an environment close to non-standard cultural and institutional experience, she wiser estimate a maximum likelihood combination that allows a group of structures that benefit various different subsets of the data control model choice. All this means that the use of game theory does not force scientists to implement a pilot model is likely to be very precise and narrow in reasonable specifications to fit the complexities of the real messy strategic interaction. It should also be applied good game view from the econometrician well educated.

4. games and coordination repeated

So now we have our attention on only  once,  and games, and that is, the games that players strategic concerns extend beyond the final decade of interaction one. However, often play games with  future  games in mind, and this can significantly alter their results and strategies of balance. And our theme in this section  is repeatedgames, that is, games that determine the players are expected to face each other in similar situations on multiple occasions. We are approaching this first through the limited context of the dilemmas that the repetition of a prisoner.

We have seen that in the PD- one shot on the NE is the only mutual split. This may be no longer have, however, if the players expect to meet each other again in the PDS in the future. Imagine that four companies, all the widgets which agree to maintain high prices by restricting supply jointly. (Ie they form a cartel.) This work unless all share the agreed production company it keeps. Typically, each company can expand its share of the profits departing while the others observe them, because then sell more units at a higher price resulting from the Union market almost intact. In the case of one shot, all companies share this incentive to defect and that the organization breaks down immediately. However, companies expect to face each other in competition for a long time. In this case, each company to know if the occurrence of the cartel agreement, others can be punished by an understatement for a long enough period for more than eliminate the gains in the short term. Of course, the punishing companies take losses very short term during their period of an understatement. But these losses may be worth taking if they serve to re-establish the organization and achieve the maximum price in the long term.

One simple, and famous (but    not, contrary to the myth of large-scale, necessarily optimal) and the so-called strategy to maintain cooperation in the PDS repeated reprisals between Sunnis and Shiites. This strategy says each player to act as follows:

  1. Always cooperate in the first round.
  2. After that, any action opponent took in the previous round.

A group of players  for  revenge play between Sunnis and Shiites will not see any cleavage. Since then, the population in terms of playing other reprisals between Sunnis and Shiites, non-reciprocal come to a rational response for each player, and everyone plays reprisals between Sunnis and Shiites is NE. You may often hear people who know  little  (but not enough) the modern game theory as if this is the end of the story. not.

There are two types of complications. First, you must be a player to end up is uncertain when they interact. Let’s assume that the players know when to come the last round. In that round, and it will be for the players to defect-maximizing benefit, because it does not punishment would not be possible. Now consider the penultimate round. In this round, the players also face no penalty split, because it expects that the split in the last round anyway. They even defect in the penultimate round. But this means that they do not face any threat of punishment in the last third round, and there is also a split. We can simply repeat this backward through the game tree until we get to the first round. Since NE cooperation is not a strategy in that round, nipple between Sunnis and Shiites no longer NE strategy repeated in the game, and we get the same result, mutual-split-as is the case in PD- one shot. Therefore, cooperation is only possible in repeated PDS where the expected number of repetitions is not specified. (Of course, this does not apply to many games and real life.) Note that in this context, any amount of uncertainty in the forecast, or the possibility of trembling hands, will lead to cooperation, at least for the moment. When people in the experiments play party got with known end points are repeated, they actually tend to cooperate for a moment, but know that the defect in the earlier they gain experience.

Now we offer Second complications. Suppose that the players ability to distinguish a split of incomplete cooperation. Look at our case cartel piece. Let’s assume that players control a decline in the market price of widgets. Perhaps this is because one of the members of the gang to cheat. Or perhaps it led to a decline in external demand. If players Tit between Sunnis and Shiites misses the second case for the first time, and will defect, thus setting off a reaction of mutual defections of which can never be healed, because every player we will reply to the first split faced with a split series, and thus begetting further defections, and so on .

If players know that this misunderstanding is possible, they have the incentive to resort to more sophisticated strategies. In particular, they may be willing to take the risk in some cases after the schism with cooperation in order to test their own inferences. However, if they are  very  tolerant, then other players can be exploited through additional splits. In general, the cutting-edge strategies have a problem. Because it is more difficult for other players to infer, their use increases the likelihood of misunderstanding. But the misunderstanding is what causes frequent balances cooperative game in the collapse in the first place. The complexities surrounding the information refers to the examination and reasoning in the PDS repeated help explain intuitively  theory popular, so-called because no one can say for sure recognized for the first time, and this in frequent PDS, on  any strategy  S  no distribution possible strategies among other things players such that the vector  S  and these other strategies is NE. Thus, there is nothing special, after all, about the nipple between Sunnis and Shiites.

Real and complex social and political drama instantiations rarely directly from simple games such as the public distribution system.  Hardin (1995)  presents an analysis of the real political cases tragically, and civil war Yugoslav from 1991-1995, and the genocide in Rwanda in 1994, as the party that had nested inside got Gamescoordination.

Game coordination is maximized whenever two or more players benefit by virtue of doing the same thing the other one occur, and whether such correspondence is more important to them than whatever it is, in particular, that they both do. For example, and “each drive on the right” arises with the standard rules of the road: “Every campaign on the left” both results NES, and it is not more efficient than the other. In coordination purely games, but do not help to balance the use of more selective criteria. For example, let’s assume that we need our players for a reason and in accordance with Article Baez (see section 3 above). In these circumstances, it is said that the adoption of any strategy is the best response to any vector of mixed strategies available in the NE to be rationalizable. That is, the player can find a set of beliefs other players such as systems that any history of the game along the path consistent with the balance that a group of systems. Featuring pure coordination games by tankers is unique rationalizable strategies. In such cases, the players have to try to predict the balances by searching for  points of contact, that is, the features of some of the strategies that they believe will be a prominent other players, and that they believe other players are believed to be leading them. For example, if two people want to face on a particular day in a big city but can not contact each other to arrange a time and place specified, both had reasonably go for the most prominent square in the city center in the city at noon. In general, the better the players know each other, or in many cases, they were able to observe each other is strategic behavior, the more likely they are to succeed in creating focal points to coordinate.

Coordination was, in fact, the first topic of game theory application which came widespread attention from philosophers. In 1969, the philosopher  David Lewis (1969)  published  the Convention, which has been the conceptual framework of the application of game theory to one of the fundamental to the theory of knowledge issues in the twentieth century, and the nature and extent of the agreements governing the semantics and its relationship to justification of beliefs my suggestion. Basic insight can be obtained by using the example of simple. And’djaj ‘word indicates the chicken and the “ostrich” shows ostrich. We will not be better or worse off if “chicken” show ostriches and “Ostrich” chicken icon. However, we  will  be worse off if half of us use a pair of words in the way the first second and a half, or if each and every one of us randomized them to refer to the birds generally fly. This vision, of course, a good run-up to Lewis. But what he catches is that this case has the logical form of the game format. Thus, while certain agreements may be arbitrary, and interactive structures that stabilize and maintain them are not. Moreover, it appears that the balance is involved in the coordination of the meanings of names have arbitrary element just because we can not Pareto ranked them; but  Millikan (1984)implies that in this regard they are atypical of language formats. It certainly atypical coordination agreements in general, a point on which misled by Louis overvalued “semantic intuition ‘about’ meaning’of” Agreement “(Bacharach 2006,  Ross 2008A).

Ross and LaCasse (1995)  provide the following example of a game of coordination and real life where the NE is not Pareto-indifferent, but more frequently observed NE- Pareto inferior. In the city, and drivers need to coordinate on one of the two NE with regard to their behavior at the traffic lights. Either everything must pursue a strategy of rushing to try to race through the lights that turn yellow (or yellow) and stop before proceeding when the red lights turned to green, or everything must follow the strategy of a slowdown in yellows and immediately jump off to switch to green . Both patterns are NE, in that once coordinated the community on one of them, then any individual has an incentive to deviate: Those who slow down on the yellows while others are rushing them back organic will, while those who are quick yellows in the other will balance the risk of collision with those who immediately jump on the greens. Therefore, once the movement pattern of the city settles on one of these balances, they will tend to stay there. And, in fact, these are two of the patterns that have been observed in the cities of the world. However, the balances are not Pareto-indifferent, since NE II allows more cars to turn left at each session in the jurisdiction left by car, and the right of each session in the jurisdiction right, which reduces the main cause of the bottlenecks in the road network urban and it allows all drivers to expect greater efficiency in getting something. Unfortunately, for reasons about which we can only speculate pending further experimental work and analysis, is embroiled in a much more cities NE- Pareto minimum of one day Pareto superior.

Agreements on scientific standards of evidence and rationality, and topics of philosophy of science that the framework for analysis Louis preparation, is likely to be for the character Barret- rankable. While different arrangements may be northeast of the game in social science, and the followers of Thomas Kuhn to remember us, it is likely that all of these are located on the Pareto-one indifference curve. These topics, strongly represented in contemporary epistemology, philosophy of science, philosophy of language, are all implicit applications at least in theory the game. (The reader can find a wide sample of applications, and references to the great literature, in Nozick (1998).)

Most of the games social and political coordination played by people they also have this feature. Unfortunately for all of us, and traps inefficiency represented NE- Pareto lowest very common in them. And sometimes the dynamics of this kind lead to the most terrible of all collective human repetitive behaviors. Harden analysis depends of the last two episodes of genocide on the idea that the characteristics of the biology of shallow people from which to sort themselves into racial and ethnic groups efficiently serve as focal points in games coordination, which in turn produces a deadly party got between them.

According to Hardin, it was a disaster none of the Yugoslav and Rwandan got the party to begin with. That is, why not in the situation, on both sides, and most people prefer to begin the destruction of the other for mutual cooperation. However, the logic killer Coordination, deliberately incited by politicians self-serving, vital  to create  the public distribution system. And it encouraged some individual Serbs (Hutu) to recognize individual interests as best work through identification with the Serbian (Hutu) group interests. That is, they found that some conditions, such as those involving competition for jobs, and the form of coordination games. Thus acted so as to create situations in which this was true for other Serb (Hutu) as well. Eventually, once is enough identified Serbs (Hutu) self-interest with a range of benefits, almost universally and become determine    the correct, because (1) was the most important goal of all Serbian (Hutu) to do almost what all the other Serbian (Hutu) would, and (2) the most distinguished Serbian  thing to do, to do that pointed coordination, and was to exclude the Croats (Tutsi). That is, it has been selected strategies involving such exclusionary behavior as a result of the existence of effective coordination centers. Making this situation is the case that the individual and the threat and Croats individually was best to maximize self-interest (Tutsi) and through coordination at the Croatian assertive (Tutsi) identity group, which has increased the pressure on the Serbs (Hutu) to coordinate, and so on. Note that it is not an aspect of this analysis indicate that the Serbs or the Hutu that things; it can be a process (even if not in fact) complete reciprocity. But the result is a horror: It seems Serbs and Croats (Hutu and Tutsi gradually) more a threat to each other as they crowd together for self-defense, until both feel that it is necessary to stay ahead of rivals and strike before being struck. If Hardin is true, and is not intended here claim that it  is, but to point out the mundane importance of identifying any agents games are actually playing, then the mere existence of the external port (NATO?) Will not have changed the game, and the speed of analysis Hobbs, since no port could be threatened both sides with nothing worse than fear from each other. What is needed is a reassessment assessments of interests, which (we can say) happened in Yugoslavia when the Croatian army began to win decisively, and at this point the Bosnian Serbs decided that the interests of the self / their group has served better by the arrival of NATO peacekeepers. Genocide in Rwanda similarly ended with a military solution, in this case the victory of the Tutsi. (But that became the seed of the bloodiest war on the face of the earth since 1945, and the war in the Congo 1998-2006).

Of course, it is not true that most games again lead to disaster. The biological basis for romance in people and other animals in part a function of the logic of repeated games. The importance of rewards achieved through cooperation in the upcoming matches lead those who expect to interact where to be less selfish than the temptation would encourage otherwise in the current games. The fact that these balances become more stable through learning gives friends logical character-based investments, which most people take great pleasure in sentimentalizing. Moreover, the cultivation of common interests and feelings provide focal points around networks can facilitate coordination increasingly.

5. Thinking Games team and a police officer

Next  (1969) Luis  enter games coordination in the philosophical literature, philosopher Margaret  Gilbert (1989)  said, as opposed to Lewis, that game theory is the wrong kind of analytical technology to reflect on human conventions that, among other problems, it is also ‘individual’, While the agreements are primarily social phenomena. More direct, and her claim that the agreements were not just a product of the decisions of many individual people, as has been proposed by the Convention on the lines of the view that as a balance to the game someone where each player one person. Similar concerns were echoed on the foundations of individual game theory by another philosopher claims, Martin  Hollis (1998)  and economist Robert Sugden (1993.2000,    2003) and Michael Bacharach (2006). In particular, it is motivated by Bacharach proposal theory  Logic team, which was completed Sooden, along with Natalie Gold, after the death of Bacharach’s. This theory is an essential part of the context of the background to appreciate the value of a large extension in the recent game theory, Wayne(2012) Stirling in  the theory of  games tied.

Again consider the prisoner’s dilemma at once, as discussed in  Section 2.4  and productive, with inverted matrix for ease of discussion later, as follows:

II
I
C Dr
C 2.2 0.3
Dr 3.0 1.1

(C indicates the strategy for cooperation with one opponent (ie, refusing to recognize) and D shows bolting to deal with an opponent one strategy (ie recognition)) Many people find it incredible when theorist game tells them that the players as standard blessed honorific “rational “You must choose in this game in such a way as to produce a result (D, D). It seems that the interpretation requires a very strong appeal to the forms of both individual and descriptive and normative. After all, if the players attached the highest value of social welfare (to society two people from thieves) of individual well-being, they can then do what is the very best individual; the game “rational” theory, and object, behavior yields This is askew even the point of an individual to improve the view. Soden (1993)  and seems to have been the first to propose that the guys who really deserve to be called “rational”, including ones is altruism, the the reason PD- one shot  as a team of one, that is, will all in their choices strategies by asking: “What is best for us? instead of” what is best for me? “.

As  Binmore (1994)  argued strongly, and it seems that most commentators later confessed, this line of criticism confused mathematics of game theory as with any questions about game theory models are most usually applicable to situations in which people find themselves. If the value of the benefit of the players they’re part of the team and narrower above their individual interests, this must be represented in the rewards associated with the game theoretical model of their choices. In similar situation as PD above, if the ‘concern’ of two players from the team “strong enough to bring about a shift in strategy from D to C, then receiving bribes in the upper left cell (interpretation cardinally) will Theo be raised to 3. At least ( at  3, players will be indifferent between cooperation and defection.) Then we get the following shift of the game:

II
I
C Dr
C 4.4 0.3
Dr 3.0 1.1

This is no longer PD. It is a  game guarantee, which has two NE at (C, C) and (D, D), with the former being a Pareto superior to the latter. Thus, if the players find this balance, we should not say that it is played in the Near East strategies PD. Instead, we should say that the PD was the wrong model for their condition.

Bacharach executors in the scientific, Sooden and gold, in  Bacharach (2006), p. 171-173), unlike Hollis and Soden (1993)  to get this right, and agreed that players can only cooperate in PD- one shot if someone makes a mistake. (For some the wrong specifications, (C, C) can arise constantly with QRE concept solution). But, Bacharach, Sooden and Gold argues, players will human game often or usually avoid framing the situation in such a way that one shot PD is the right model for their circumstances. The situation in which agents “odd” that the framework for PD can also be governed by “thinking” as factors to ensure the game above the transition team. Note that the care team may make a difference for (Cardinal) bribes without  enough  of a difference to outweigh the temptation to split from one side. Suppose it bumped it to 2.5 for each player. Then the game will continue to PD. This is an important point, because in the experiments the subjects play a sequence party got at once (not  repeated party got, especially as the opponents in experiments change from round to round), the majority of subjects begin through cooperation, but learning to defect also offers tests. Bacharach on account of this phenomenon, these issues framing the start of the game as the team reasoners. However, the minority of subjects frame it as individual reasoners and defect, profit-taking free riders’. Reasoners team and then re-framing the situation to defend themselves. And enters this critical aspect of Bacharach’s account. Reasoners individual and team reasoners that different types of people are not claimed. People, and maintains Bacharach, flip back and forth between individual agency and participate in the agency team.

Now consider the following game Pure format:

II
I
C Dr
C 1.1 0.0
Dr 0.0 1.1

We can interpret this as a situation in which players are the individual narrow, and therefore all indifferent between NE two (U, L) and (D, R), or are reasoners team but did not admit that their team is the best off if stability around one of the NE instead of the other. If they did it come to such a recognition, perhaps by finding a focal point, and then are converted game Pure coordination in the next game known as  hello, if:

لاعب II
لاعب I
T1 T2
S1 10,10 0.0
S2 0.0 1.1

Crucially, here’s transformation requires more than  just  thinking about the team. Players also need to know the focal points of any two of the pure balances coordination offers the possibility of less risky to achieve social stability (Binmore 2008). In fact, Bacharach and his executors are interested in the relationship between the pure coordination games and games hello, if for some special reason. It does not seem to imply any criticism of NE solution as a concept he did not favor one strategy tankers on the other in a game of pure format. However, NE also  not in favor of the selection (U, L) to (D, R) in the game hello, if it depicts, because (D, R) is also NE. At this point Bacharach and his friends rely philosophical logic to program refinement. Sure, complaining, “rationality” recommends (U, L). Therefore, they conclude, it must be built axioms for the team to think of refined theory of the foundations of the game.

We do not have to support the idea that it should refine the game theoretical concepts solution to accommodate the general concept of intuitive rationality to stimulate interest in the contribution of Bacharach. Can a game theorist is psychological propose a precise shift of focus: instead of worrying about whether our models should respect the base team focused rationality, we may simply refers to the empirical evidence that people, and perhaps other factors, it seems that making often Options that reveal the preferences that are conditional on the well-being of the groups to which they relate. To this extent their agency partially or totally, and perhaps randomly identified with these groups, and this will need to be reflected when we were their own agency model using utility functions. We can best describe the theory as a theory we want to choose a team focus rather than theory Logic team. Note that this philosophical interpretation is consistent with the idea that some of the evidence we have, and maybe even the best evidence we have, the presence of the selection team is centered psychotherapy. It is also consistent with reference to the processes that face people between the individual and team-centered agency and is latent in part. The point is simply that we do not need to follow Bacharach thinking about game theory as a model of logic or rationality in order to be persuaded that it has identified a gap we would like to have a formal resources to fill the void.

Therefore,  not  people’s choices seem to reveal a team-centered preferences? Standard examples are drawn, including Bacharach, ranging from sports teams. Members of these teams under great social pressure to choose actions that increase the likelihood of victory over the actions that increase personal statistics. The problem with these examples is that they are difficult to include identifying problems with regard to estimate utility functions. Player narrow self-interest who wants to be popular with the fans may behave in conformity with the team focused. Soldiers in battle conditions more convincing examples. Despite trying to convince soldiers to sacrifice their lives in the interests of their own countries often ineffective, can cause most of the soldiers to take extraordinary risks in the defense of their comrades, or when enemies directly threatened their towns and their families. It is easy to think of other types of teams that most people are reasonably identify some or most of the time: a set of projects, small businesses and local trade unions, clans and families. Strongly individual social theory trying to build teams such as the balance in the individual games among the people, but not assume a solid game theory (or, for that matter, the prevailing economic theory) imposes this perspective. We can assume instead that these teams are often welded externally into being by the psychological and institutional operations complex and interrelated. This calls on the scene depicting sports game that mission does not consist in modeling logic team, but in the choice of models that are conditional on the existence of the dynamics of the team.

This brings us to the  (2012) Stirling in  the extension of game theory to cover such conditional interactions. Target Stirling is formalizing, and extraction equilibrium conditions for, an idea that preference group that is, on the one hand, and not just a compilation of individual preferences, but also do not, on the other hand, simply assume collective existence transcendent and that are imposed on individuals. Intuitive Stirling has a goal in mind is that the processes that people derive their preferences actual results in part on a comparison basis to take care of a range of different possible configurations of preferences that individual members can reveal theoretically. A Stirling is a key constraint to respect the concepts of the theoretical solution (ie unbalance him)) must officially mainstream  notions of the standard solution (NE, SPE, QRE), and not replaced. Supposed to be a “real” game theory, not “false” game theory conditional game theory.

Let’s develop an intuitive idea of conditionalization preference in more detail. People may often perhaps usually, to postpone the full decision to their preferences until they get more information on the choices of others who are his colleagues in the team’s current or potential. Stirling itself provides a simple (it can be said is very simple) example of  Kenny and Raiffa (1976), which is one of the farmers is a clear preference between the different climatic conditions for the purchase of land only after, and partly in light of his wife and learning preferences. This little thought experiment is plausible, but not ideal as an example because it is integrated easily with vague concepts, we may entertain fusion  Agency ideal in marriage, it is important to distinguish between the dynamics of conditionalization preference in the agents featured teams from a simple  breakdown of  individual agency. So let’s imagine, for example, the better. Imagine consult her about the Council of risk-averse about whether it should continue to be a serious attempt to acquire President companies. A comparison of possible actions it may be used: in the process of (i) send it to every member of the Council through individual e-mail about the idea of a week before the meeting. In the process (II) that it originates them en masse  in  the meeting. Most people will agree that the two processes may yield different results, and that the main reason for this is that in the process (i), but not (b), and some members may reinforce personal opinions that they do not have time to settle in case they received information about one ready to time to challenge the president in the audience at the same time that they heard the proposal for the first time. In both processes imagined there, when voting points, groups of individual preferences to be assembled by the vote. But it is likely that some of the preferences in the group that was created by the second operation was  conditional  on the choices of others. Stirling unconditional preference as it determines the preference is that the information about the preferences of affected (specified) others.

A second idea officially in Stirling theory is compatibility. This refers to the extent of the controversy or dispute that a set of preferences, including a set of conditional preferences, would generate if the implementation of balance among them. Or members of the team leaders do not always want to achieve the maximum compatibility through all internal engineering games, warranty or hello, if (even though it probably always want to eliminate the PDS). For example, a manager may wish to encourage the degree of competition between profit centers in the company, while he wants cost centers to identify completely with the team as a whole.

Stirling formally known theories of representation of the three types of utility functions is: conditional interest, utilities are identical and identical conditional interest. This can be applied repeatedly, any individuals, to teams and teams from the difference. Then the essence of development is the official theory that combines conditional identical preferences of individuals to build models to choose the team that does not impose externally on the members of the team, but instead stems from several preferences. To say the procedure assembly Stirling in the current context, it is useful to change the terminology to him, and therefore reformulation of him rather than quote directly. This is because the Stirling refers to “groups” instead of “teams”. Stirling does not mention the work of Bacharach, so do not put his theory in the context of logic team (or what can be re-interpreted as an option centered team). But ideas Bacharach provide a natural environment in which to frame the technical achievement Stirling as enriching the application of game theory in the social sciences. We can then reformulate his five restrictions on the assembly as follows:

(1)  conditioning: may be affected, he said team member preference Sort by the other team members of Preferences, which may be conditional. (impact may be set to zero, in which case the conditional order of preference breaks down to preference categorical demand of the RPT Standard).

(2)  establish internal: it is necessary to identify and arrange for a coordinated team work through the social interactions of sub-teams. (This requirement ensures that the preferences team simply does not impose on individual preferences).

(3)  Acyclicity: social impact relations are not reciprocal. (This is likely to seem at first glance to be a strange constraint: relations impact certainly the most social, among people in any case, is  reciprocity, but, as noted earlier, we need to keep the distinct unconditional agent fusion preference, this requirement helps. to do this. And most importantly, for the math because it allows teams to be represented in the graphs of the directives. The condition is not restrictive, where you feel the flexibility of modeling, as one might think in the beginning, because it only prevents us from agent representing  the  affected another agent  and I’m from  directly  influencing    i we are free to represent. j  as influential   as, which in turn affects i.)

(4)  exchange: Buy identical preference is fixed under representative transformations which are equivalent with respect to information about preferences conditional orders.

(5)  the monotony in sound: If the sub-group and one prefer to choose alternative A to B and all the other sub-teams are indifferent between A and B, then the team does not prefer B to A.

Under these restrictions, Stirling prove the theory of the assembly which follows the overall result for the completion of facilities in light of new information that has been developed by  Abbas (2003, Internet resources and other). Individual team members for each preference group account by grouping identical conditional preferences. Then applies analyst marginalization. Allow XN Team be. Allow XM= {XJ 1, …، XJ m} And X= {XI 1, …، XI k} It is separated from the sub-teams XN. Then the tool concrodant marginal for help XM With respect to sub-team {XM، XK} It is obtained by collecting more aK, Resulting in

InSM(aM) = SaKInSMSK(aM, AK)

The marginal benefit of the individual team member XI Given by

InSM(aM) = S~ ForIInSN(to1, …, ForN)

Where blogging S.~ ForI It means that the amount taken all the arguments only aI (Stirling (2012), p. 62). This process produces  an unconditional  preferences of individual  i  former thereafter, have been updated in the light of her identical conditional preferences and information that described them, two identical conditional team preferences. Once Each subsequent options and agents account, and games which led to that are involved can be solved by standard analysis.

Stirling is building, he says, the real generalization of the theory of the standard benefit, so as to make an unconditional (“categorical”) the benefit of a special case. And it provides a basis for the formalization of the benefit of the team, which can be compared with any of the following actions: blunt instrument pre-conditioned by the individual sub-team or; tied to an individual or subgroup utility; or tool identical conditional sub-group individual or assistance. Once it has been marginalized in the preferences of each individual problem of choosing the team, NE, may be proposed SPE or QRE analysis on certain solutions to the problem of full information about the social impacts. Can not be solved using the incomplete cases relieved Nash or serial balance information.

6. Commitment

In some games, the player can improve its results by taking actions that make it impossible for her to take what could be her best work in an interview at one time to move the game. It referred to such procedures as obligations, and that it can serve as alternatives to external enforcement in the games that will settle only on balances Pareto inefficient.

Consider the following hypothetical example (which is  not  of PD). Let’s say you own a piece of land adjacent to mine, and I would like to buy it in order to expand a lot to me. Unfortunately, you do not want to sell at a price I’m willing to pay. If we move one at a time, I publish the selling price and a separate I give my agent there price-demand there will be no sale. So you might try to change the incentives by playing the opening step in and I would like to announce that I will build a sewage plant smell of rotten on the ground next to you only if you sell, and thus stimulates you to lower your price. We have now turned this game in a sequential step. However, this step until now does not change anything. If you refuse to sell in the face of my threat, then it is not in my interest to do them, because in the damage you also like to hurt myself. Since you know this must ignore my threat. My threat not true, a case of cheap talk.

However, I could make it occurred to me credible by  committing  myself. For example, you can sign a contract with some promising farmers to provide them with water sewage treatment (fertilizer) from my station, but including a penalty clause in the contract to release me from my duty only if you double my lot size and so put to some other use. Now my country is a reliable threat: If you do not sell, I am committed to building a sewage plant. Since you know this, you now have an incentive to sell me your land in order to escape from ruin.

This type of situation presents one of the many fundamental differences between the logic of non-parametric and expand the border. In border cases, it can never be an agent worse off by having more options. (Even if the new option is worse than the options that began, she can be ignored.) But where conditions are not a border, could be one agent strategy affected for another person if the options were confined clearly. Cortez burning his boats (see Section 1) is, of course, this is unprecedented, and one who works to make the usual metaphor literal.

Another example illustrates this, as well as through the application of the principles of game types. Here we will build an imaginary situation is not PD- since only one player has an incentive to defect, but that is a social dilemma as far as NE in the absence of non-Pareto’s commitment to its lowest result can be achieved  with  for your commitment. Let’s assume that the two of us are interested in hunting rare antelope from a national park in order to sell the cup. One must chase us down the animal toward the second person, who is waiting in the blind to shoot it and load it on a truck. I promise you, of course, to participate in the revenue with me. However, the promise is not credible. Once you’ve got a buck, you have no reason not to drive it away and pocket the full value of it. After all, I can not complain very well to the police without getting myself was also arrested. But now suppose I add the following step to open the game. Before our hunt, and manipulation of the truck with alarm that can only stop of punching in the code. But I know the code. If you try to push back without me, the audio alarm and we’ll both get caught. , With this knowledge, and now an incentive to wait for me. What is critical to note here is that you  prefer  that I rode the alarm, because this makes your promise to give me my share credible. If you do not do this, and let your promise in credibility, we will be able to agree to prosecute the crime in the first place, and both of us will lose an opportunity for us in the profit from the sale of the cup. Thus, you can benefit from my point of view prevents you from doing what is optimal for you in the subgame.

Are we now to combine our analysis of the distribution of food rations and hardware system commitment to discuss the application that for the first time the famous game theory outside the academic community. In the nuclear confrontation between the two superpowers during the Cold War studied at length by the first generation of game theorists, many of whom worked for the US military. (See  Poundstone 1992  to get the historical details.) Has maintained both the United States and the Soviet Union the following policy. If one side launched a first strike, and some threatened to answer with devastating Counter-Strike. This pair of joint strategies by the late 1960s knew was actually meant to blow up the world, and “mutual destruction”, or “MAD”. Game theorists objected that MAD was crazy, because the establishment of PD result of the fact that mutual threats were incredible. Gold underlying causes of this diagnosis as follows. Suppose that the Soviet Union launched the first strike against the United States of America. At this point, the US president finds his country had already been destroyed. He did not bring it back to life, which even now blowing in the world, so he has no incentive to carry out its threat to avenge the original, which is now clearly failed to achieve points. Since the Russians to expect this, we should ignore the threat of retaliation and the first strike. Of course, the Americans are in a completely symmetric mode, so they also must be the first strike. Each authority recognizes this incentive on the part of the other, and so will expect an attack if they do not rush to pre-empt it. Thus, what we should expect, because it is the only NE in the game, it is a race between the two to be the first to attack.

This analysis is the theory of the game caused real panic and fear on both sides during the Cold War, and is famous for its attempts produced some striking in the establishment of the strategic commitment devices. Some tales, for example, claims that President Nixon had the CIA in an attempt to convince the Russians that he was insane or drunk often, so they think it is better retaliatory strike even when it is no longer in his interest to do so. Similarly, the Soviet KGB claimed to have fabricated medical reports overstated aging Brezhnev with the same end in mind. Eventually, the symmetry of strategic interest to analysts, the US Department of Defense complex and possibly breaking changes in tactics deployment of US missiles. It is equipped with a fleet of submarines all over the world with enough missiles to destroy the Soviet Union. Make this a less reliable network of contacts directly, and thus introduced an element of uncertainty related strategically. President probably can be less sure to be able to reach the submarines and cancel orders to attack if any Soviet missile radar exceeded the trigger line in northern Canada. Of course, this value in breaking the symmetry rely on the Russians to be aware of this potential problem. In the classic Stanley Kubrick film  Dr.  Strangelove, it is the destruction of the world by accident because the Russians build a doomsday machine that will automatically result in a retaliatory strike regardless of their own leadership’s determination to follow through on the threat implicit MAD but then keep it a secret. As a result, when it launches mad colonel unequivocal American missiles in Russia on its own, the US president is trying to convince his Soviet counterpart that the attack was unintentional, and Russian Prime Minister says shyly about his secret device Day of Resurrection. Now the two leaders can do nothing but watch in dismay as the world is blown up because of game theory is wrong.

This example of the confrontation of the Cold War, while great fame and importance in the history of game theory and popular reception, adopted at that time in analyzes that were not very accurate. The military theorists game will almost certainly wrong to the extent that they along the lines of the Cold War as a PD- one shot in the first place. For one thing, and enmeshed in a game of nuclear balance in the world’s major athletics a great deal of complexity. On the other hand, it is not clear that either superpower, the other with annihilation avoid self-annihilation was in fact the result of a higher rank. If you do not, in one or both cases, then the game was not PD. A cynical wisdom may suggest that researchers operations on both sides were playing a cunning strategy in the game over the funding, one of them containing cooperate with each other in order to convince politicians to allocate more resources to weapons.

In mundane circumstances, most people everywhere commitment device that exploits the Adam Smith long ago made ​​the focus of his theory of the social order: the value to the people of their own reputations. Even if I am secretly stingy, I might want to cause others to think of me generous by tipping in restaurants, including restaurants that I did not intend to eat again. Whenever I do this kind of thing, the more I invest in reputation values ​​which I can strongly hurt by one of the clear reaction, noted, it means Nice. Thus my reputation hard-earned functions as a mechanism generosity commitment in certain games, in itself impose the continuation of reinvestment. In time, it may become my usual goodness, and therefore insensitive to changes in circumstances, so much so that the analyst has no remaining justification for the continuation of the experimental model in preference to me the existence of scarcity. There is a great deal of evidence that this hyper-social behavior of humans is supported by the biological behavior evolved (found in most, but not all people) suffer emotionally from negative gossip and fear of it. As people get rid of course to  enjoy gossiping, which means that punish others by spreading the news when their commitment is a form of social police, who do not find expensive and HE confronted devices fail. A nice feature of this kind of punishment is that it can, unlike the (opinion) hitting people with sticks and be withdrawn without leaving long-term damage to punishee. This is a happy property of the device that has a point to contribute to the maintenance of the common social entrepreneurship incentives; cooperation is generally more fruitful with his teammate, who is not broken bones. Thus forgiveness agreements also play a strategic role in this mechanism is very elegant commitment that natural selection was built for us. Finally,  standards  have evolved culturally mutual expectations in a group of people (or, for that matter, elephants or dolphins or apes), which has another characteristic that individuals who violate them may punish itself  by feelings of guilt or shame. And therefore they may often take cooperative action against the narrow self-interest even when no one is interested. Religious stories, or those pseudo-philosophical involving Kant “rationality”, is likely to be told, especially in explaining the rules of the game because the basis of the theory of the source does not happen to people.

Although the so-called “emotions’are moral extremely useful to keep a commitment, it is not necessary to do so. Humanitarian institutions is the largest, famous, high obtuse morally. However, the commitment of a very important is usually to their own logic and functional. For example, tempt the government to negotiate with terrorists to secure the release of hostages in certain occasion had committed “line in the sand” strategy in order to maintain a reputation for toughness aimed at reducing incentives for terrorists to launch attacks in the future. The progress is different from, for example type by Qantas Airways in Australia. Qantas has suffered Never a fatal accident, and for a period (until it suffered some incidents of non-fatal embarrassing that are likely afraid to draw attention) make a lot of this in their advertisements. This means that the aircraft, at least during that period, and probably  was  safer than average, even if the Only the initial advantage a little bit of good statistical fluke, because the value of being able to claim a perfect record grew longer continue, and so gave the airline incentives continuing to incur greater costs to ensure safety. probably still has an incentive to take extra care to prevent the recorded deaths from crossing the line Reputation magic between 0 and 1.

Certain conditions must hold if the effects are the reputation of the underwriting commitment. First, it must be repeated game. Rating has no strategic value in the game at once. Second, the value must be greater reputation for its agriculture of the value of his sacrifice in  any  particular round of repetitive game. Thus the players to establish a commitment by reducing the value of each round so that the temptation to defect in any round did not get high enough to constitute a temptation hard to resist. For example, the parties to the contract may exchange obligations in small increments to reduce the incentives on both sides of repudiation. And therefore construction companies may pay to build on a weekly or monthly payments projects. Similarly, the International Monetary Fund often distributes loans to governments in small segments, thus reducing the incentives for governments to violate the terms of the loan as soon as the money is in hand. And governments may actually prefer such arrangements for the removal of internal political pressure are not compatible for use of the money. Of course, we are all familiar with cases where the payoff of a split in the current round becomes very large relative value over the longer term, of a reputation for collaboration in the future, we wake up to find that the cashier community has absconded overnight with the funds. Commitment by ensuring the reputation of the cement is in the community, but any such natural bonding agent to be away from completely effective.

7. evolutionary game theory

Gintis (2000,  2009) feel justified in saying that “the theory of the game is a universal language to unite the behavioral sciences.” There are good examples of this unified action. Binmore (1998,  2005A) social history models in the form of a series of convergence on the effective balance increasingly in games deal encountered, interspersed with bouts in which some people try to shift to new balances that kicks off paths stable balance , leading to periodic disasters. (Stalin, for example, tried to turn his community for a set of balances that allow people cares more about the future of industrial, military and political power of the state that they care about their lives was not successful; however, his efforts certainly created a situation in which, for several decades, and many of the Soviet people attach much less importance to  other  life than usual.) Moreover, applications of game theory to topics behavioral extends beyond the political arena. In  Section 4, for example, we saw Lewis recognition that all human language amounts to a network of Nash equilibrium in games coordination on the transfer of information.

Given his vintage, and restrict Louis fixed his attention to game theory, which are modeled as agents deliberately  choose  a certain fixed interest strategies and functions externally. As a result of this limitation, account some philosophers called to follow the misguided pursuit of general analytical theory of rational agreements (as noted  Bickhard 2008). Although Ken Binmore criticized this focus again and again through the worthy profession in contributions (see references to a selection),  Gintis (2009)  have recently isolated the fundamental problem with a certain clarity and perseverance. NE and SPE are  fragile  concepts of the solution when applied to the natural evolution of computational mechanisms such as animal (including human) minds. As we have seen in  Section 3  above, in coordination (and other) games with multiple NE, what is the logical economic sense for the player to do is very sensitive for countries to learn from other players. In general, when they find themselves in games where the players did not have the dominant strategies accurately, they have only incentives uncomplicated to play NE SPE or strategies to the extent that the other players are expected to find her  NE or SPE strategies. Can  the public  be expected reasonably rational strategic theory, the kind that philosophers have sought to cover emergency situations arising? Resorting to the principles of Bayesian logic, as we reviewed in  Section 3.1, is the standard way to try to integrate this uncertainty to the theories of rational, strategic decision. However, as  Binmore (2009)  shows all the beautiful and clear in a recent book, Bayesian principles is not valid only  as rational principles themselves  in the so-called “small worlds”, this is the environments in which they are quantified risk distribution in the range of known and enumerable parameters , as is the case in our solution game cross the river from  Section 3. In the big world, where utility functions, sets strategy and structure of the media is difficult to estimate and subject to change through potential external influences, and the idea that the rule of Baez tells the players how to ‘be rational “implausible quite. But then why should we expect players NE to choose or SPE or sequential equilibrium strategies?

As  Binmore (2009)  and Gintis (2009) all of the stress, and if the game theory is to be used in the actual model, natural behavior and its history, outside of the small world settings which microeconomists (but not the overall economy or scientists or scholars of political sociology or philosophers of science) mainly traffic , and then we need some account of what is attractive about the balance in games even when the analysis can not be seen through the tame uncertainty in such a way that it can be represented as pure risk. That once again refer to the subject of Lewis, human language evolved when there was no external rule to care about and take the necessary arrangements for Pareto efficiency by providing a contact point for coordination. About what people agreed, within the linguistic communities, to use almost the same words and constructions to say similar things. It seems unlikely that any, strategic planning explicit deliberate on the part of anyone who played a role in these processes. However, game theory turned out to provide the basic concepts to understand the stability of languages. This striking Gintis support for optimism about the reach of the game theory point. To understand this, we must expand our attention to the  development of  games.

Game theory has been applied fruitfully in evolutionary biology, where they are dealing with the types and / or players genes, since the pioneering work  Maynard Smith (1982)  and his collaborators. Evolutionary (or dynamic form) game theory now new sports accessory large applies to many of the settings apart from the biological.  Skyrms (1996)  uses evolutionary game theory in an attempt to answer the questions Louis could not even ask, about the circumstances in which the language and concepts of justice, the the concept of private property, public and other non-designed phenomena of interest to philosophers are likely to arise. What is novel about the game is that the evolutionary theory did not choose moves through deliberation by individual agents. Instead, they usually wired are agents diligently with certain strategies, and is defined as the success of the strategy in terms of the number of copies of himself that he will leave to play in the games of the future generations, given the number of people that other strategies which it works are distributed to certain frequencies. In this type of setup problem, the same strategies the players, and individuals who play these strategies are just the perpetrators who get their costs and benefits associated with the immediate results of the operation.

The discussion here will be closely following and Skyrms. We start by presenting  the dynamics refined. First consider how the work of natural selection to change the lineages of animals, modify, and create and destroy species. The basic mechanism is the  reproduction differential. Any animal with  inherited features that increase the  expected number of offspring  in a particular environment will tend to leave more offspring than others as long as remain relatively stable environment. It would be likely to inherit the features in this issue of the offspring. Therefore, the ratio of these features in the population will gradually increase with the passage of generations. Some of these features may  go to install, that is, in the end to take all the population (even the environment changes).

How game theory in this intervention? Often, one of the most important aspects of the organism environment are behavioral tendencies of other objects. You can think of all proportions to “try” to maximize its reproductive fitness (= expected number of grandchildren) through the creation of strategies that are optimized due to the strategies of other lineages. Even the theory of evolution is another area of ​​application of the non-parametric analysis.

In the evolutionary game theory, we no longer think about the choice of strategies for individuals as they move from one game to another. This is because different interests. We are now less concerned with finding a balance from one Games from the discovery that a stable balance, and how they will change over time. So we now model  the same strategies  also play against each other. One strategy is “better” than the other if they are likely to leave more copies of itself in the next generation, when the game will play again. We study the changes in the distribution strategies in the population as games unfold relay.

Of evolutionary game theory, we offer a new concept of balance, because of  Maynard Smith (1982). There are a range of strategies, some in a certain percentage (for example, 1/3: 2/3, 1/2: 1/2, 1/9: 8/9, 1/3: 3/1: 6/1: 1/6 always summarize 1) are still in  You to ESS  (stable evolutionary strategy) balance just in case (1) Any person who plays one strategy can improve the reproductive fitness by switching to one of the other strategies in the ratio, and (2) does not play mutant completely different strategy can establish itself (‘invasion’) in the population.

Best explain the principles of evolutionary game theory through examples. Skyrms begin by investigating the circumstances in which a sense of justice for the purposes of understanding the specific analysis and disposition to view sections of equal resources as fair as efficiency considerations did not refer only in special cases, may arise. It asks us to consider a number of individuals in the population regularly with each other and must bargain for resources. Start with three types of individuals:

  1. Fairmen  We demand always exactly half of the resources.
  2. Greedies  always demanding more than half of the resources. When they encounter another greedy greedy, and wasting resources in more fighting.
  3. Modests  always calls for less than half the resources. When other marks modest modest, they take less of all available resources and lost some.

Each  one  to meet the demands of reaching the amount to 100% of the NE is an individual game. Similarly, there can be many vital balances. Suppose that Greedies claim 2/3 of resources and demand Modests 1/3. Then the following two ratios are for ESS:

  1. Half of the population is greed and a half modest. We can calculate the average payoff here. Modest gets 1/3 of the resources in each encounter. Greed gets 2/3 When you meet a modest, but nothing when you meet another greedy. So her average yield also 1/3. This is because of Fairman ESS can not be invaded. When he meets Fairman gets a modest 1.2. But when he meets Fairman greed it gets nothing. So his return on average is only 1/4. Not modest to have an incentive to change strategies, nor does any greed. The mutant Fairman emerging in the population is doing worse than all, and so will choose not encourage the spread of such mutants.
  2. All players Fairmen. Everyone always gets half of the resources, and no one can do better by switching to another strategy. Greedies enter this meeting Fairmen population and get the average yield of 0. Modests get 1/3 as before, but this is less than the payoff Fairman of the half.

Note that the balance (i) ineffective, as the average yield across a smaller population. However, just as non-effective results can be fixed NE of games, so they can be in the ESS of those evolutionary.

We refer to the balance that occurs more than one strategy also forms. In general, in a game Skyrms, and any polymorphism which demands greed  tenth  and the demands of a modest 1- X  is the ESS. The question that raises student justice regards the relative likelihood that these various balances arise.

This depends on the proportions of the strategies in the case of the original population. If the population began with Fairman more than one, then there are some possibilities that Fairmen will face each other, and get the highest possible return on average. Modests in itself does not prevent the spread of Fairmen. Greedies just done. But Greedies themselves dependent on the presence Modests about in order to be viable. So the more Fairmen there in the population for the  pairs  of Greedies and Modests, and Fairmen do better on average. This involves a threshold effect. If Fairmen decreased less than 33 percent, then the tendency will be for them to fall to extinction because they do not meet each other often enough. If Fairmen population rises above 33%, then the tendency will be for them to rise to install because the additional gains when they meet each other compensate for their losses when they meet Greedies. You can see this by observing that when each strategy is used by 33% of the population, all of which are expected to yield an average of 1/3. Therefore, any increase above this threshold by Fairmen tend to push them towards the installation.

This result shows that and how, given some relatively general conditions and justice as we set that  can be created dynamically. News of the masses of Justice gets more cheerful still If we offer  a play interrelated.

Model we saw just assumed that the strategies are not linked, meaning that the probability that each strategy meets every other strategy is a simple function of the relative frequency in the population. Now consider what happens in a dynamic game division of the resources we have when we link. Suppose that Fairmen have a slight ability to differentiate and look for other partners Fairmen interaction. In this case, Fairmen, on average, do better, and this must have an impact on lowering the threshold for going to install.

Game evolutionary link Modeler effects and other border restrictions by running a large computer simulation strategies which compete with each other studies, round after round, in a virtual environment. Ratios ranging from strategies, and any degree chose link, simply can be placed in the program. One can monitor the dynamic unfold with the passage of time, and measuring the proportion of time it stays in any one of balance. These are percentages of the relative sizes  of the basins attractions  for different balances possible. Balances are the attractive points in a dynamic space; basin attractions for each point and then a set of points in space and that of the population will converge to the equilibrium in question.

The introduction of a link in his model, Skyrms first determine the degree of correlation in a very small 0.1. This causes the basin of attraction for the balance of (i) to shrink by half. When the link is set to 0.2 degrees, a swimming polymorphic reduces to the point where people start to polymorphism. And therefore very slightly in a relationship produces large proportional increase in the stability of equilibrium where everyone plays Fairman increase. A small amount of the link is a reasonable assumption in most of the population, given that neighboring countries tend to interact with each other, and mimic each other (either genetically or because of tendencies to deliberately copied each other), and because of genetically similar animals culturally more likely to live in common environments. Thus if justice can arise in all that will tend to be dominant and stable.

A large part of the political philosophy consists in attempts to produce a standard deductive arguments designed to persuade the agent unjust that they have reasons to work for justice. The analysis indicates Skyrms completely different approach. We will do our Fairman everyone in the game dynamic if it takes effective steps to maintain the link. Thus, there is evolutionary pressure for each of the  ethical approval to justice only institutions that arise. Most people may think that 50-50 divisions are “fair”, and their value by maintaining the moral and institutional reward and sanctions,  because  we are dynamic game promoted by our tendency to think in this way products.

The topic that has received the most attention from evolutionary game theorists is  altruism, which is defined as any behavior by an organism that reduces fitness own projected in one interaction, but more than that of the interactor to another. It is common to say in nature. How can arise, but in view of the Darwinian competition?

Skyrms studies this question using the prisoner’s dilemma dynamic as his example. This is just a series of games played in the PD population, be from among its members and dissidents, some of whom are members of the collaborators. Bribes, as is always the case in evolutionary games, measured in terms of the expected number of copies of each strategy in the coming generations.

Let  U (A) the average fitness of the strategy  A  in the population. Let  U  be the average fitness of the total population. Then strategic proportion  A  in the next generation is just the ratio of  U (A) / U. Even if  A  has a fitness greater than the average population increase. If  A  has a fitness less than the average population, and  A decreases.

PD in terms of interaction and dynamic random (ie there is no link), the dissidents do better than the average population as long as there are collaborators around. This is evident from the fact that, as we have seen in Section 2.4, cleavage always prevailing strategy in one game. And thus 100% cleavage is the ESS in a dynamic game without the link, corresponding to the NE at one shot PD constant.

However, the introduction of the possibility of radical change in the correlation image. Now we need to calculate the average fitness strategy  given the likelihood to meet each other strategic fit. In evolutionary PD, collaborators who meet the high probability of other partners do better than dissidents who face the prospect of other dissidents high. And therefore prefer to link cooperation.

In order to be able to say something more precise about the relationship between the association and cooperation (and in order to be able to tie the game for the issues of evolutionary theory in decision theory, an issue outside the scope of this article), Skyrms introduces a new technical concept. It calls the strategy  ratification adaptation If there is an area around the installation point in the vital space like this from anywhere within that region will go to install. In evolutionary PD, both cleavage and cooperation and endorsement of the adaptation. The relative sizes of the basins attract highly sensitive to certain mechanisms by which to achieve the link. To illustrate this point, Skyrms builds several examples.

One of the models Skyrms to enter the link through  the liquidation of  the pairing interaction. Suppose that in round 1 of PD dynamic individuals lose each other and interact, or not, depending on what they find. In the second and subsequent rounds, all individuals who have not been paired in round 1 are paired randomly. In this game, and attract a large basin to split  unless  there is a high proportion of the collaborators in one round. In this case, the dissidents fail to associate in round 1, then get paired mostly with each other in round 2 and push each other to extinction. Model which is more interesting, because the mechanism is less artificial, does not allow for individuals to choose their partners, but requires them to interact with those close to them. Because of genetic kinship (or cultural learning copies) individuals are more likely to resemble their neighbors who do not. If this was arrayed (limited) population within one (ie along the line), and provided all of the collaborators and dissidents in positions along at random, then we get the following dynamics. Collaborators be less isolated fitness expected of dissidents surrounding a locally endangered move. Members of the two groups of collaborators have a 50% probability of interaction with each other, and the potential for 50% of all interaction with the dissidents. As a result, their fitness is not expected average still smaller than that neighboring dissidents, and they are also facing the threat of possible extinction. Groups of three members of the cooperatives form the unstable point that each of extinction and the expansion is likely both. However, one meeting in groups of four or more collaborators at least collaborator collaborator with sufficient guaranteed at least replace the original group. Under these circumstances, and collaborators as a group do better than surrounding defectors increase and at their own expense. Eventually collaborators go  almost  to install, but not completely. Dissidents and one on the sidelines of the population prey to collaborators at the ends and stay alive “criminal groups” minimal. And therefore we do not see can be maintained that altruism only by the dynamics of evolutionary games, but, with a link, even originally can be deployed and the colonization of the population is altruism.

And therefore the dynamics of Darwinism offers qualified good news for cooperation. Note, however, that this holds only as long as individuals are stuck with the natural or cultural programming, and can not re-evaluate their own facilities. If our agents to get too clever and flexible, and they have noticed they’re in the PDS and all will be better off defecting. In this case, they will end up paying for themselves in danger of extinction unless working to develop a stable and ethical standards, and effective work to promote cooperation. But, of course, this is only what we expect to develop in the population of animals that are closely linked to the social capabilities of successful cooperation average fitness levels. Even in light of this, these populations go extinct, but they care about the future generations for a reason. But there is no logical reason why agents  should be  interested in future generations if each new generation completely replace the previous one at each change cohorts. For this reason, economists use ‘overlapping generations models when modeling the distribution games. Individuals in generation 1, which will continue until the 5th generation to generation resource conservation 3 individuals who they would like to cooperate; and generation 3 new members care about the 6th generation; and so on.

Gintis (2009)  says that when we set out to use evolutionary game theory to unify the behavioral sciences, we start using to unify the theory of the game itself. We pointed out in several previous points in this article that the NE and SPE concepts to solve the problem in many applications where the rules are clear institutional clients missing because they have incentives to play NE or SPE only to the extent that they are confident that other factors will follow suit. To the extent that agents do not have such confidence – and this, by the way, is in itself because of the idea of game theory – what should be expected is a general social disorder and confusion. Gintis shows in detail how the key to this problem is the presence of what he calls “the choreographer. By this means that some external elements, which has agents for any balance strategies should expect others to play. As discussed in  Section 5, cultural norms are probably the most important designers dance for people. He studied with an exciting benefit of the interest which includes the criteria of the kind relevant to a wide range of jobs Bicchieri (2006). In this context, Gintis indicates the unification of more great importance element: If agents attach a positive benefit to the following choreographer proposals ( that is, to being linked strategically with others for great it), and then wherever the competing potential rewards do not overwhelm this incentive, can also be expected to estimate constantly priors Bayesian, and thus achieve a balance in beliefs, as discussed in the agents  section 3.1 , the lack of information in the Games.

In light of this, when we wonder about the value of game theory models in the application of human behavior outside markets well-organized, and a lot depends on what we take to be reasonable and validated experimentally sources people incentives to coordinate with each other. This has been the recent subject of considerable debate, which we will review in  section 8.3  below.

8. Game Theory and Evidence behavioral

In the previous sections, we review some of the problems that arise from the classic treatment (non-evolutionary) game theory as a theory standard that says to people what to do if they wish to be rational in strategic situations. The difficulty, as we have seen, is that there seems to be no concept of a single solution we can recommend unequivocally for all situations, especially when the agents private information. However, in the previous section we have shown how to appeal to the foundations of evolution sheds light on the circumstances in which the functions of the tool that was a reasonable explicitly can be applied to groups of people, leading to the game theoretical models with reasonable and stable solutions. So far, we have not reviewed any actual empirical evidence of behavioral observations or experiments. Game theory and experimental researchers have already contributed to new discoveries about the behavior (human or otherwise)? If so, what in general, and the content of these discoveries were?

In addressing these issues, we face the question of which is the direct knowledge. There is no way for the application of game theory “on its own”, apart from the other modeling techniques. The use of standard terminology in the philosophy of science, one can model game theory to the phenomenon only in conjunction with “assumptions help” test on this phenomenon in question. At least, that if one follows strict about the treatment of game theory as a mere mathematics, with no empirical content of its own. In one sense, a theory with any empirical content never open to the test at all; one can only worry about whether the axioms which is based on the theory of mutually consistent. However mathematical theory can be evaluated with respect to the experimental interest. One type of philosophical criticism that was sometimes made of game theory, interpreted as a mathematical tool for modeling the behavioral phenomena, that is always applied or usually requires the use of false or misleading or simplistic strongly on such phenomena assumptions. This criticism we expect to have varying degrees of strength in different contexts of the application, and assumptions differ help.

Until things turn out. There is no room for interesting applications that game theory was not completely unlike him. However, there was no easier in general consensus on how to use game theory (both classical and evolutionary) to understand the behavior of non-human animals of focusing on how to interpret the dissemination and forecasting of the strategic activities of the people. Let us first consider the brief philosophical and methodological issues that have arisen on the application of game theory in biology non-human period, before devoting attention to complete the game-theory of Social Sciences.

Dish controversial modeling less than the classical form of the theory to look at strategies that non-human animals seeking basic resources related to the evolutionary tournament: opportunities to produce offspring that are themselves likely to multiply game theory. And therefore in order to achieve maximum fitness expected, you must find the optimal trade-offs between different animals intermediate goods, such as nutrition and security of predation and the ability to compete outside of his rivals for his teammates. Efficiency trade-off points between these goods can often estimated for certain types in certain environmental conditions, and on the basis of these estimates, both parametric and nonparametric balances can be drawn. Models of this type has a proven track record in predicting and explaining the experimental data independent of that strategy phenomena as foraging competitive, choosing a mate, nepotism and the rivalry between brothers and grazing and collective anti-predator vigilance and signals, mutual grooming, and reciprocity between species (Takaful). (For examples see  Krebs and Davis in 1984,  Bill 1991,  Dugatkin and countryside in 1998,  Ducasse in 1998, and Noah, Van Hove and Hammerstein   2001). On the other hand, as Hammerstein (2003)  notes and reciprocity, exploitation, and metaexploitation, and much more rarely seen in non-human animals of the social game theory modeling will lead us to imagine. One explanation for this is that the proposed Hammerstein non-human animals and usually have less ability to restrict their interaction partners of people are doing. Our discussion in the previous section of the importance of interdependence to achieve stability in the game Solutions lends theoretical support for this proposal.

Why helped classic game theory to predict the behavior of non-human animals more directly than I did most of human behavior? Is supposed to be the answer lies in the different levels of complexity of relations between the assumptions assistance and phenomena. Ross (2005A)  provides the following account. Utility-maximizing and fitness problems to maximize the field of economics. And determine the economic theory with clients to maximize the areas of economic units preference change. The identification of individuals with the whole diversity of these factors is more acceptable and less sophisticated cognitive organism. Thus insects (for example) are easy to apply revealed preference theory specially designed (see  section 2.1). The nervous system has also become more complex, however, we are faced with the animals learn. Learning can cause a sufficient degree of permanent changes in the behavioral patterns of the animal we can preserve the identity of the individual with a biological agent and one around the amendment only on the vacuum demonstration account (the functions of the various utility functions, increase ad hoc). Moreover, the increasing complexity confounds the development of simple models on the second dimension: Animals sophisticated cognitive change not only their preferences over time, but is governed by control operations distributed that makes the competition sites between  internal  agents (Schilling 1980;  Ainslie 1992,  Ainslie 2001). And it is therefore not economic factors and clear even  at  a time. In going out to model the behavior of people who use any part of the economic theory, including game theory, we must realize that the relationship between any particular person, an economic factor and build for the purposes of modeling will always be more complex than a simple identity.

There is no sudden crossing point which becomes cognitively advanced animal also to be modeled as an economic one, and all animals (including humans) and there are contexts in which we can ignore useful simultaneous dimension of complexity. However, we are facing a phase shift in the dynamics of modeling when we move from asocial animals to social issues is eusocial. (This refers to animals that are social, but that does not, cases such as ants, bees, wasps and termites and rats naked mole, and to do so thanks to the cooperation to fundamental changes in the genetics of its population that make individuals within the groups to clones edge. Home-known are the parrots, corvids and bats, rats, dogs, hyenas and pigs, raccoons, otters, elephants, hyraxes, cetacians, and monkeys) in their cases, the stability of the dynamics of the internal control partly located  outside individuals and at the level of the dynamics of the group. With these creatures, and modeling of the individual economic agent, with the function of a single comprehensive tool, it is a radical idealization, which can only be done with the greatest caution and systematic attention to the specific contextual related to the exercise of certain factors modeling. Game theory is that applications can only be empirically adequate to the extent that economic models are inadequate experimentally.

Homo sapiens  is an extreme case in this regard. It is controlled in individual human beings socially to a degree unknown in any other species eusocial. At the same time, large cognitive plasticity that allows them to vary significantly between cultures. People and therefore less economic factors and clear of all living organisms. (And so can believe that it is ironic that were taken, originally and for many years, to be the ideal conditions of economic agency.) Will look at the implications of this for game theory applications below.

First, however, it needs to be clarification on the adequacy of the experimental  development of  game theory to explain and predict the distribution of strategic actions in the population and agents. These models are applied both for the animals as products of natural selection (Hofbauer and Sigmund 1998), and social animals is eusocial (but not particularly humans) as products of cultural selection (Young 1998). There are two assumptions help one must justify, for a particular case at hand, in building such applications. First, one must be a cause for confidence that the actions of one seeking to interpret are (either biological or cultural, as the case may be) the amendments -mn is, actions that have been identified and are retained because of the way they promote their own fitness or physical fitness of a broader system, rather than an accident or by-products which are inevitable structurally from other amendments. (See  Dennett 1995  public discussion of this issue). Second, one must be able to put the enterprise modeling in the context of justification of assumptions about the evolutionary relationships between overlapping operations on different time scales group. (For example, in the case of a species with cultural dynamics, how the development of hereditary slow restrict the rapid cultural evolution? How cultural feeding evolution is due to the genetic evolution, if it is fed back at all? Clear to discuss the highest of these issues, see Sterelny 2003 .) conflicting views about any of these assumptions should be made ​​about human evolution is the basis of the current differences in the game live evolutionary modeling of behavior and behavioral theory of human institutions. This is where the issues in evolutionary game theory converge issues in the burgeoning field of  behavioral experimental  game theory. Therefore I will mention first the second field before closing this article by giving a sense of the differences just alluded to, and which are now vital field of philosophical argument in the foundations of game theory and its applications.

8.1 game theory in the laboratory

Economic theories have been tested by running laboratory experiments with human and other animal material since pioneering work  Thurstone (1931). In recent decades, it has become the size of this huge work positively. The vast majority of it and identify materials in the problem of micro-economic environments able to compete minus. Because this is exactly the situation that the partial collapse in game theory and experimental economics was the most experimental game theory. Thus it is difficult to distinguish between experimentally motivated by questions about the adequacy of the empirical microeconomic theory and empirical questions about the adequacy of the theory of the game.

Here we can only give a broad overview of the massive and complex literature. Readers are referred to the pending polls in  Kagel and Roth (1995),  Camerer (2003),  Samuelson (2005), and GUALA (2005). There are high-level principle useful to sort indexes literature to help the various assumptions that are applied game theory axioms. It is often said in the People’s presentations (for example,  Ormerod 1994) that experimental data are generally the hypothesis that people are rational economic agents refute. These claims are not very accurate to be sustainable interpretations of the results. All the data are consistent with the view that people approximate  economic factors, at least for periods of long time enough to allow the game theoretical analysis of specific scenarios, meaning the minimum that their behavior can be modeled in harmony with preference detection theory (see  section 2.1). However, RPT makes very little in the way of experimental demands that this is not nearly as surprising as much non-economists that (Ross  (2005A). What is really at issue in many of the discussions about the general interpretation of the empirical evidence is. To what extent people to achieve the maximum benefit from the expected and as we have seen in Section 3, the expected utility theory (EUT) is applied in general along with game theory for cases involving uncertainty – model, which means that most of the attention and behavioral. science However , a variety of mathematical calculations alternative to maximize suitable for the von Neumann-Morgenstern cardinalization of benefit; and will be invited empirical adequacy of game theory in question unless we thought that people’s behavior is not generally described by Cardinal VNMufs on the interpretation of a liberal suitable for this (ie, as opposed to interpretation VNM who knows the narrow interest of precisely where the EUT).

What empirical literature appears to show really is a world of behavior that is very ‘chaos’ from the perspective of the scene point of view. And chaos in the question that arises from the lack of significant heterogeneity, both among people and between (a person, and situation) tankers. No one from the family of optimization functions exist so that people act so as to maximize a member of that family in all circumstances. I learned a good face problems in contexts that are not unduly demanding, or that people are very organized institutionally often behave like maximizing expected utility. General reviews the evidence and theoretical issues, see  Smith (2008) and Binmore (2007). An extended sequence of examples of empirical studies, see what experiences called “double auction constant” discussed in the  Plott and Smith in 1978  and Smith 1962.1964, 1965.1976, 1982. As a result, the classic game theory can be used in these areas with high reliability to predict the behavior and implementation policy, as evidenced by dozens of highly successful auctions of government facilities and other assets designed by game theorists to increase public revenues (Binmore and Klemperer 2002).

In other contexts, and interpret the behavior of people as expected-utility maximization requires undue violence to the principle of parsimony in theory building. We get a better prediction using less assumptions If we assume that the topics to maximize according to one or typically- more  of several alternatives (which will not be described here because they are not directly about game theory): a copy of the probability theory (Kahneman and Tversky 1979), or Alpha Theory Nu interest (Qiu and MacCrimmon 1979), or the expected benefit with the possibilities that depend on the rank of the theory (Quiggin 1982,  Yaari 1987).  Harrison and Rutstrom (2008)  show how to design and code  the maximum likelihood mixture models which allow the designer experimental models for the application of a combination of these jobs decision and one set of selection data. Output ratio of the total selection analysis and determines the best explanation of each model in the mixture group.  Anderson  et al.  (2014)  take this approach to the current state of the art, which shows the experimental value, including the model of non-maximizing-latent psychological proceses in a mixture along with maximize the economic models. This new flexibility with regard to effective decision modeling that can be deployed in the practical applications of game theory reduces most of the pressure for changes in game theory structures themselves. Thus it fits perfectly with the interpretation of game theory as part of the mathematical tools in the behavioral world, rather than an experimental model of the first class of the human psyche.

A more serious threat to the usefulness of game theory is evidence to the contrary systematic preferences, in both humans and other animals. This is more dangerous both because it exceeds the human condition, and it challenges the theory of revealed preference (RPT) rather than just excessively strict commitment to the EUT. As described in  Section 2.1, RPT, unlike the EUT, the foundations of game theory is obvious explanation is psychological. (Not all writers agree that the apparent phenomena preference reverse threaten RPT instead of the EUT, but see the discussion in Camerer (1995), pp. 660-665, and.  Ross (2005A), pp. 177-181.) A foundation for setbacks preference seems to be are common in animals with brains is  hyperbolic discount for the future (Strotz 1956, Ainslie 1992). This is the phenomenon where agents discount future rewards more sharply in the current close to the reference point of the remote distances of time distances of time. The best way to understand this contrast with the idea found in most traditional economic models of exponential  discount, in which there is a linear relationship between the rate of change in the distance to the bonus and the rate at which the value of the reward signal low point. The following figure shows the exponential and hyperbolic curves for the same period from a point of reference to return in the future. One down graphic function hyperbolic charges; bowed shape results from a change in the discount rate.
Figure 15

The result of this is that, as the prospects for a later come closer to the point of consumption as possible, people and other animals sometimes will spend undo the consequences of his actions prior to that also cost them resources. For example: today’s report, whether to celebrate a pile of academic articles or watch a baseball game, and procrastination, despite knowing that by doing so I put access to more fun some prospect to come for tomorrow (when there are equally attractive ball game on if The best option) did not arise. So far, this could represent a way that maintains the consistency of preferences: if the world may end tonight, with a very small probability, but non-zero, then there is a certain level of risk aversion that you’d rather leave the articles completely unmarked. This figure compares less than two exponential curves of the opponent, and one drop of the value of watching the game before the completion of my marking, high and one of the game I enjoy more value after completion of the work. Both of which have a higher value than the reference point to him as soon as they are; but the curves do not cross, so my preferences revealed consistent with the passage of time no matter how impatient I may be.
Figure 16

However, if committed myself against procrastination by buying a ticket for tomorrow’s game, when in the absence of an awful task I had not done that, then I have been violated time consistency preference. More clearly, it was in a position to choose last week whether the stall today, you may choose not to. In this case, my deduction drawn from the reference point last week expressing curve drawn from the perspective of today, and my preferences opposite curve. The following figure shows this situation.
Figure 17

This phenomenon is the complexity of the classic game theory of intelligent applications for the animals. However, it obviously does not invalidate it completely, because people (and other animals) often  do not  reflect their preferences. (If this is not true, the successful auction and other models of nights called “mechanism design” would be ambiguous.) Interestingly, the leading theories that aim to explain why the hyperbolic discount may often act in accordance with RPT themselves appeal to the game principles theory.  Ainslie ( 1992,  2001) account of the people and communities of interest bargaining Interior, which micro-units on a short-term basis has produced, facing the medium-term and long-term conflict that must be resolved because if they do not do so and instead create internal collapse Hobbs interests (section 1), external agents that avoid the results of Hobbs can destroy them all. device tyrant Hobbs is not available to the brain. Therefore, its behavior (when it is madness to avoid system-level) is a series of balance imposes itself of the kind studied by game theory of public choice literature on bargaining coalition in the Democratic legislatures. This means that domestic politics in the brain is the “mutual concessions” (Stratmann 1997). Then the organization of the internal dynamics of these partially stabilized from a broader social games which are an integral part of coalitions (people as companions on the subparts time of their CVs) (Ross 2005A, p. 334-353). (For example: social expectations about the role of someone as an equilibrium position of the goals of behavioral processes mutual concessions in the brain salesperson) is likely this adds other elements relevant to explain why and how stable institutions with relatively transparent rules are the basic conditions that help people more like economic factors are clear, such as the classic game theory find reliable application of their entire units.

One important note of caution is in order for the reader here. Many of the recent behavioral literature takes for granted that timetable discount contrary is the case or the default standard for the people. However,  Anderson et al.  (2008)  show experimentally that this arises from (i) on the assumption that groups of homogeneous people with regard to which forms of functional best description opponent behavior, Wu (ii) not to raise and control the various standards of the people independently of risk aversion in estimating the discount functions. In a group of the population that have been studied with these two considerations in mind, the data indicate that a fixed discount chronologically describes the much higher proportions of options than it does contradict timetable options. Then you should avoid excessive generalization of the models hyperbolic discount.

8.2 nervous economics and game theory

The notion that game theory could find a new application for the internal dynamics of the brains, as proposed in the previous section, has been developed from separate motives by new research known as program neuroeconomics  (montage and Burns 2002,  Glimcher 2003,  Ross 2005A, p. . 320-334,  Camerer, Weinstein and Prelec 2005). Thanks to new technologies scanning non-invasive, and especially functional magnetic resonance imaging (fMRI), recently became possible to study synaptic activity in the brains of work while they respond to stimuli controlled. This new path has allowed access despite what is still one of the very indirect(Harrison and Ross, 2010) – from the brain to calculate the expected values ​​of the bonuses, which (of course) have been taken to play a crucial role in determining behavior. Economic theory is used to frame the derivation functions maximized by synaptic level account of the expected values; and therefore “neuroeconomics” name.

Game theory play a leading role in the science of the nervous economy on two levels. For the first time, it has used game theory to predict the calculations that neurons and groups of neurons that serve individual reward system must implement. In the example the best media,  Glimcher (2003)  and his colleagues that the monkeys be that they are trained to play the so-called “Games inspection against resonance computer magnetic career scanned computers scanned. In Game inspection, one player is facing a series of options either to work for a reward, in this The situation is sure to get them, or for the performance of another, and work easier (“evasion”), in which case you will get a bonus only if another player (and “Inspector”) does not monitor him. Assume that (“worker”) player behavior The first reveals the function of the tool bordered on each end as follows: he would work for every occasion If the inspector is always watching and it is decoy on every occasion will if the Inspector monitors never. inspector would prefer to get the maximum amount of work for the lowest monitoring price possible. In this game and NE only for both players in conflicting strategies, because no pattern in the one player that can be detected by some to be tapped strategy. for any particular pair of defined benefit for two players functions meet the restrictions mentioned above, any pair of strategies that, for all trial, either the worker is indifferent between work and evasion or inspector is indifferent between monitoring and not monitoring, and is NE.

Game application analyzes of pairs or groups of inspection agents requires us to be  either justified independently functions useful to all relevant variables to their play, and in this case we can define NE and then test to see whether maximizing expected utility successfully;  or  to assume that they maximize the benefit expected, or obedience to another rule such as matching function, and then infer the usefulness and functionality of their behavior. Either this procedure could make sense in different experimental contexts. But the increase cognitive influence significantly if it is to determine the function of utility inspector externally, because it often. (Implementation of the inspections police on the side of a random way to catch drunk drivers, for example, it is usually the maximum driving rate be drunk allocated to them as a target by the policy, and the budget set externally. These determine the function of its usefulness, given the distribution of preferences and attitudes to risk among the population of drivers.) In the case of experiments and Glimcher Inspector is a computer, so the pilot program under control and is known as its side of the matrix reward. Agents expected topics of interest, “in this case Fountains of fruit juice for the monkeys, can be determined in a former parametric test settings. Then the computer is programmed with the economic model of the Apes, and can search the data in their behavior in the circumstances of the game to use patterns, strategic varying accordingly . With this fixed, NE expected utility maximization by monkeys can be calculated and tested by manipulating the computer’s utility function in different runs of the game behavior variables.

Monkey behavior after training tracks NE very strongly (as does the behavior of people playing games similar cash prizes.  Glimcher 2003, pp. 307-308.). Working with trained monkeys, Glimcher and his colleagues can then conduct experiments of importance here. Work and evasion behaviors of monkeys may associated with training staring either to the right or to the left on the visual display. In previous experiments,  Platt and Glimcher (1999)  established that in parametric settings, bonuses juice vary from one block of tests to another, firing rates of each neuron mural, which controls eye movements can be trained to encode the expected benefit for monkey of all possible relative movement of the expected movement of interest alternative. Thus “movements which were worth 0.4 ml of juice twice as strongly represented [in the probability of neural firing] as movements worth 0.2 ml of juice” (p. 314). Not surprisingly, when different amounts of juice reward each movement of one block of tests to another, firing rates also varied.

Against this background, Glimcher and colleagues can be achieved in the way the brains of monkeys “carried out follow NE. When I played the monkeys Game inspection against the computer, and can specify the target associated with the evasion in the perfect location, because of the training prior, nerve cells specific under study, while the objective of the will appear in the empty place. This allows Glimcher to test the answer to the following question: Are the monkeys preserved NE in the game by keeping the firing of nerve cells fixed rate while the actual behavior and optimized for monkey whole variety? data gave a strong answer is “Yes”. Glimcher explains reasonably this data limit on it indicates that the neural firing rates, at least in this cortical to this important region, encoding the expected benefit in each of the parametric settings and nonparametric. Here we have a clear justification for the practical application of the theory of the classic game in independent institutions or social norms context .

Pay further analysis deeper hypothesis. The Inspector playing computer with the same sequence of results also received her opponent monkey to play the previous day, and each step he was asked to assess the expected values ​​of the relative evasion and procedures available in the next step. Glimcher a positive relationship between small fluctuations around the stable rates NE at reports of firing of individual neurons and expected values ​​estimated by the computer in an attempt to follow the same NE. Glimcher comments on this result as follows:

It seems that the neurons to reflect that, based on the play-by-play, and close the account to the one carried out by our computer … [A] ta … [relatively] … on a microscopic scale, we were able to use the theory of The game begins in the description of the decision-by-decision calculations that neurons in LIP performing area. (Glimcher 2003, p. 317)

Thus, game theory that go beyond its traditional role as a technique to frame the high-level constraints on the dynamics of development or behavior by agents familiar with working in corporate straightjackets. In the hands of Glimcher, and are used for the activity of a typical directly in the brain of a monkey.  Ross (2005A)  says that groups of nerve cells and thus the lines should not be identified with the units playing semi-personal that I found in the theory Ainslie bargaining within the personal described earlier. That would involve the kind of experience that a simple reduction in the behavioral sciences and life has taught us not to expect. The issue has arisen since then in direct conflict between neuroeconomists more competing interpretations of observations fMRI to choose the time and the discount (McClure  et al. 2004),  Glimcher and others.2007). The weight of the evidence favors yet to that if it is sometimes useful to analyze people’s choices as balance in the matches between the sub-agents and personal, should not determine personal sub-factors in question with separate areas of the brain. The other explanation is, unfortunately, still the most common in the literature less specialized.

We have now seen the first level in the science of the nervous economy, which is applied game theory. The second level involves variables conditioning is seeking in neural activity that may affect people’s choices strategies when playing games. This has usually included a repetition of the protocols of the game behavioral theory of literature with research subjects who are lying in the optical fMRI scanners during play.  Harrison (2008)  and Ross (2008b) has defended the skepticism in the work of this type value, which include various uncomfortable leaps large inferred from the behavior of the observed link with specific neural responses calculated. It can also be asked whether the acquisition of a lot of new knowledge generalizable to the extent that these associations  can  be determined successfully.

Let’s provide an example of this type of “game in the scanner” – involving direct strategic interaction  King Casas and others. (2005)  Took a standard protocol of behavioral game theory, or the so-called game of “trust”, and its implementation with subjects ‘brains were scanned together using technology to connect the functional maps of the brain each of them, known as the “hyperscanning’). This game involves players two. In Fig. Frequent is also used in King Casas and others. experience, he was appointed the first player in the “investor” and the second “guardian.” investor starts with $ 20, which she can keep any part of its option while investing the rest with a guardian. in the hands of Guardian is three times the amount invested by the experimenter. guardian may then return as much or as little of this profit to the investor as it deems appropriate. run the procedure for ten rounds, with players’ identities remain unknown to each other.

This game has an infinite number of NE. Previous data from behavioral economics consistent with the claim that the NE unconditional in human play  about  both players using the “Tit between Sunnis and Shiites” strategies (see  Section 4) modified by defections from time to probe for information, and some cooperation after the split, which the payroll (limited) tolerance From these investigations. This is the result of very weak, because it is compatible with a wide range of assumptions on exactly what Tit differences between Sunnis and Shiites are used and continuous, and thus permits no conclusions about the possible dynamics under various educational conditions, institutions, or cross-cultural transfer.

When he ran this game under hyperscanning, the researchers interpreted the remarks as follows. Neurons in the caudate nucleus and the guardian (generally to perform calculations or midbrain dopamine systems outputs) believed it was believed that a strong response shows investors when mutual trust is that in truth, responded to a split with the increase of the vineyard. As the game progresses, it is believed that these responses have shifted from being reactionary to being anticipatory. It has been inferred profiles and reputation so as predicted by classical game theory models may be constructed directly from the brain. Another aspect of these results can not be predicted by theoretical modeling alone, which is purely may behavioral observation were not sufficient to distinguish, and was taken to be that the responses of neurons guilty to malevolent reciprocity, that is, have registered cooperation generosity in response to much smaller in Capacity. The assumption was that the mechanism by which the brain performs modification Tit between Sunnis and Shiites are in order to prevent defections from time to time to check information from disintegration cooperation on a permanent basis.

Progress in the understanding that practitioners of this style of neuroeconomics hope consists not in what tells us for certain types of games, but in comparison easy inferences about the ways in which the contextual framing affects people guessing about the games that they were playing. FMRI or other types of investigations of minds working may be conjectured, it will enable us to quantify the degree of strategic surprise. Mutual interaction expectations for the surprise may be subject to the same strategic manipulation, but this is an idea that has barely begun to be explored theoretically by game theorists (see  Ross and Dumouchel 2004). Some neuroeconomists believe that we now have the possibility of a pilot test new theories such as this, instead of just modeling them in theory, may stimulate growth in this type of research.

8.3 game theoretical models of human nature

And it reviewed the developments in the previous section to bring us up to the border moving from the experimental applications / behavioral classic game theory. We can now return to the branch point stopped several vertebrae, where this stream of investigation to meet the next game of evolutionary theory. There is no serious doubt, as compared with other non-eusocial animals -pma our closest relatives, chimpanzees and bonobos, humans achieve amazing feats of coordination (see  Section 4) (Tomasello  et al. 2004). A lively controversy, with important and fought on both sides with the arguments of game theory philosophical implications, currently rages about the question of whether this ability can be fully interpreted by the cultural adjustment, or explained better by inference to the genetic change early in the career of  H. sapiens.

Henrik others. (2004,  2005) and run a series of experimental games with a population drawn from fifteen of human communities on a small scale in South America, Africa and Asia, including three sets of foragers, six sets of sellers slash and burn, and four groups of nomadic herders, and two sets of small-scale farmers. Games (warning, the dictator, public goods) that it has implemented all subjects place in situations similar to the widespread confidence that the game that have been discussed in the previous section. That is, alarm and public goods games are scenarios in which the social welfare can be enlarged and well-being maximized every individual (efficiency Pareto achieved) if and only if some players at least use strategies that are not sub-game strategies perfect balance (see  section 2.6). In games dictator, the first engine selfish narrow pick up all the profits available. Thus, in every type of match three, players will SPE who cared only about their own care cash to get the results that will include bonuses that do not achieve equality too. In any of the communities studied by Henrik others. (Or any other community that has been playing games of this type) These results are observed. Players who have roles are such that they will take away all but the epsilon of cash dividends if the partners played SPE partners always provided much more than epsilon, and even then sometimes partners reject such offers at the expense of receiving any money. Moreover, unlike traditional materials experimental economics university students in industrialized countries-Henrik  others in. Subjects did not even play a  Nash  equilibrium strategies with respect to monetary rewards. (That is, players strategically fortunate divisions offered greater strategic those from disadvantaged profit was necessary to induce agreement to its offerings.) Henrik others. The interpretation of these findings by suggesting that all the actual people, as opposed to “rational economic man”, the results of the value of equality to some extent. However, their experiences also show that this limit varies greatly with culture, associated with variations in the specific cultural variables: typical bribes Cooperation (over the economic life of the community depends on the cooperation with kin indirect) and total integration of markets (a building built independently calculated degree of social complexity, anonymity, privacy, and the size of the settlement). As the values ​​of these two variables increase, transitions game behavior (weak) in the direction of Nash equilibrium play. Thus, the researchers concluded that people are genetically endowed with a preference for equality, but the relative weight of these preferences for programming through social learning processes conditional local cultural cues.

Henrik in the evaluation of    others. The interpretation of this data, we should note first that there is no axioms RPT, or of different models of the decisions mentioned in Section 8.1, which are applied jointly with a game theoretical modeling of the data of human selection, determines or consequences of selfishness property narrow. (See  Ross (2005A)  Chapter (4);  2005b Binmore ()  and (2009); and any economy or game text which allows math theory do the talking and not insist on ‘spinning’ in idealogical or another direction.) Orthodox game theory and therefore is not expected that people will play SPE strategies or NE derived by treating cash bonuses equivalent to interest.  Binmore (2005b)  therefore justified in taking Henrik others. The most important of the familiar rhetoric suggesting that the experimental work embarrass the traditional theory. it does not.

This does not mean that the anthropological interpretation of experimental results should be taken as indisputable. Binmore (1994, 1998, 2005A,  2005b) have argued for many years, based on a wide range of behavioral data, that when people are playing games with non-relatives, they tend to learn to play the Nash equilibrium with respect to utility functions that are compatible with nearly of the functions of income. As he points out in  (2005b)  Binmore, Henrik others in. Data do not test this hypothesis for small-sized communities, because their subjects were not exposed to the test matches for the (very long, in the case of a deadline for the game) you know that the period of theoretical and computational models indicate required for people to converge on the NE. When people play games is familiar, they tend to model them by reference to the games they are used to in everyday experience. In particular, they tend to play games one laboratory batch as if they were familiar with  the repeated  games, since a single shot games are rare in normal social life outside the institutional contexts. Many of the explanatory remarks by Henrik others. This is consistent with the hypothesis relating to their subjects, even though they refuse to explicitly However hypothesis itself. What is controversial here, the issues revolve around the “orthodox” theory aside, what is less certain topics, in this experiment they did about what their behavior should lead us to the conclusion about human evolution.

Gintis (2004),  (2009)  argues that the data of the kind that we have discussed support for the following conjecture about human evolution. Our ancestors to achieve pure maximum of individual fitness. Somewhere along the evolutionary line has reached the grandparents in the circumstances in which to be enough of them to the fullest extent to fit individual fitness by maximizing his group (Sober and Wilson 1998) that genetic modification went to install species: we put preferences not only their own individual our social welfare, but over the relative well-being of all members of our communities and indexed social standards  of programming  in each individual through cultural learning. And therefore it advised the contemporary researcher application of game theory in the design of social case to detect with utility issues have jobs model by (i) to know what the community (or communities) are members, and (b) the conclusion utility function (s) programmed into the members of this community (communities ) through the study of representatives of each community in the relevant range of games and on the assumption that the results are balances format. Since utility functions are dependent variables here, and games must be determined independently. We could normally be held for at least the strategic forms of games with fixed link, Gintis supposed, by virtue of (a) our confidence that people prefer the results of equality, everything being equal, for those that do not achieve equality in the ‘group from the inside “culturally evolved they see themselves as belonging and (b) the condition that the balance of the game is drawn from the stable attractors in the evolutionary game theory models of reasonable historical dynamics and culture.

Condition (b) as a constraint on game theory models of the overall strategy of human behavior it is no longer very controversial – or, at least, no more controversial than adaptationism year in evolutionary anthropology which is one expression. However, some commentators are skeptical about the proposal Gintis that there was a break in the genetic evolution of human social behavior. (For the cognitive evolutionary anthropology that explicitly denies this outage, see  Sterelny 2003). Partly based on these doubts (but more directly on behavioral data) Binmore (2005A,  2005b) people resist modeling the presence of a built-preferences in equality.According to (Binmore in 1994, 1998,  2005A) model, the core layer of the strategic problems facing social animals is eusocial is coordination games. human societies evolve cultural norms to determine the balance in these games, and many of these balances will be compatible with high levels of behavior apparently altruistic in some (not all) games. Binmore says that people adapt to their perceptions of justice for all that happens to be the rules prevailing locally choose their own balance. However, he insists that the  dynamic development of these standards must be compatible, in the long term, with balances bargaining between individuals with regard to the self. In fact, he says that as societies evolve institutions that promote what Henrik others. Call overall market integration (discussed above), and utility functions and social norms tend to converge on the economic rationality on the self in relation to social welfare. This does not mean that Binmore pessimistic about the prospects for equality: he develops a model showing that Almsomon communities on a large scale self-interest naturally can be pulled along the paths stable balance vital to the distribution of the approved rules of justice Rawlsian (Rawls 1971). The main barriers to this development, according to Binmore, are precisely the kinds of preferences for the other conservatives that valuation as a means to discourage the study of more equal bargaining balances that are at hand along the balance of societies paths.

Resolution of this debate between Gintis and Binmore Fortunately you do not need to wait on the discoveries about the human evolutionary past deep that we have never. Experimental models make predictions competition from some measurable phenomena. If Gintis is right then there is a limit, imposed by the discontinuity in the evolution of hominid, the extent to which people can learn to be self-regarding that. This is the main significance of the controversial discussed above through Henrik  and others. And interpretation of field data. Binmore model in the selection of social balance also depends, in contrast to Gintis, the behavior on a large scale among the people to inflict the second division as punishment for community members who fail to punish violators of social norms.  Gintis (2005)  shows using the game model theory that this implausible if it costs a big penalty. However,  Ross (2008A)  says that the assumption widely in the literature that the punishment of rules and standards violation results must be expensive than non-discrimination adequately between models of the original of the evolution of social behavior, on the one hand, and models of the maintenance and development of rules and other institutions It has stabilized initial set of them. Finally, Ross also points out that Binmore goals are as standard as much as descriptive: it aims to show the egalitarians how to diagnose errors in rationalization to maintain the status quo programs without calling for revolutions that put stability equilibrium path (and thus, social welfare) at risk. Is the principle of sound in the construction of reform proposals which should be a “scoundrel proof” (as Hume said it), that is, it must be compatible with less than altruistic may  prevail in people. Thus, despite the fact that the majority of researchers working on the foundations of game theory of social organization at the present time appear to side with Gintis and other members of Henrik others. Team, an alternative model Binmore has some strong considerations in its favor. Here, then, is another question along the border of game theory application is pending a decision in the coming years.

It has developed a huge range of applications both more classic game and the theory of evolution, but now we hope we have enough to convince the reader of the enormous, and is constantly expanding, this analytical tool useful. The reader’s appetite for more, which has raised should find that now has sufficient understanding of the basics to be able to work through a large literature, which are some of the following key points are listed.

index

Annotations

In the following section, books and materials that no one is seriously interested in game theory can be marked with (**) to miss.

Textbook at the most affordable cover all the main branches of the theory of the game is to  Dixit, Skeath and Reiley (2009). It should be quite a new student to the field to work through this before moving on to anything else.

Game theory has applications are endless, and that this article was able to suggest only a few. Readers looking for more than that, but I do not want to immerse themselves in mathematics, and can be found on a number of good sources.  Dixit and Nalebuff (1991)  and (2008)  are strong especially on the political and social examples.  McMillan (1991)  confirms business applications.

Great historical breakthrough, which was officially launched the theory of the game is to  von Neumann and Morgenstern (1944), and that those scientists interest in game theory should read the classic papers of  John Nash (1950a, 1950b, 1951). A very useful key underlying securities, all the classic, is  the fact that (1997). Contemporary sports for the treatment of which is an unusually sophisticated philosophical,  Binmore (2005c) (**) in a class by itself. In the second half of  Kreps (1990)  (**) is the best starting point available for a tour of the fears surrounding the philosophical choice of balance normativists’s.  Koons (1992)  takes these issues. Fudenberg and Tirol (1991)  still is the most comprehensive full text of sports available.  Gintis (2000) feet (**) text overcrowded workouts wonderful problem, which is also unique in that it addresses the evolutionary game theory for the provision of the founding basis of the theory of the game in general. Recent developments in the basic theory well represented in  Binmore, Kerman and Tani (1993). Anyone who wants to apply game theory to real human choices, which is usually associated with randomly and not inevitably to optimize axioms, needs to understand quantial response theory (QRE) as a concept solution. Found on the original development of this in McKelvey and Palfrey (1995)  and Miklvi and Palfrey (1998).

Are presented philosophical underpinnings of the basic concepts of game theory as economists understand them in  LaCasse and Ross (1994).  Ross and LaCasse (1995)  outline of the relations between the games and axiomatic assumptions microeconomic and macroeconomic. And discusses the puzzles philosophical on this serious foundation level in  Bicchieri (1993)  (**). Lewis (1969)  puts balance the concepts of game theory to practice on a wider scale in the philosophy, though, take some basic assumptions is technically correct. The program is also a good deal, and without repeating the Constituent errors, which  Skyrms (1996)  (**) and (2004). (See also Nozick [1998]).  Gauthier (1986)  launches literature does not surveyed in this article, which is investigating the possibility of the foundations of game theory to the ethics of contractarian. This work explored decisively in  Vallentyne (1991), and spread to the central dynamic in  Danielson (1992). Binmore (1994 and 1998)  (**), however, effectively destroyed this project. You will also find philosophers  Hollis (1998)  to be of interest.

In a class by itself on the insight, originality, and the importance of reading and cross-disciplinary work is the winner of the Nobel Prize Thomas Schelling. It is the source of great literature that applies game theory of social and political issues that are directly related, and shows how minor it possible to wear one if the logic of mathematics is to make sure the feet enough. There are four volumes, each basic:  Schilling (1960)  (**), Schilling (1978/2006)  (**),  Schilling (1984)  (**), Schilling (2006)  (**).

Harden (1995)  is one of many examples of the application of game theory to problems in applied political theory.  Baird, Gertner and Picker (1994)  uses a review of game theory in legal and jurisprudential theory. Mueller (1997)  surveys applications in political economy.  Ghemawat (1997 )  does the same in business strategy.  Poundstone (1992)  offers a lively history of the prisoner’s dilemma and used by strategists of the Cold War.  Durlauf and Youth (2001)  is a good group on the application of social structures and social change.

Evolutionary game theory condemns the emergence of outright  to Maynard Smith (1982)  (**). Text of the game which integrates directly with the theory of biology, see  Hofbauer and Sigmund (1998)  (**). Sigmund (1993)  offers these materials in the form of a less technical and more accessible. Some of the exciting applications of evolutionary game theory to a range of philosophical issues, which this article has developed dramatically, is  Skyrms (1996)  (**). These issues are discussed seriously and others from different angles in Danielson (1998). It presents mathematical foundations of evolutionary games in  Whipple (1995), and further consideration of the  Samuelson (1997). As mentioned above,  Gintis (2000)  (**) now offers a primer that takes the modeling of evolution to be the foundation for all of game theory.  The HP Young (1998)  gives the sophisticated models of the dynamics of development of cultural norms through the game interactions factors with cognitive abilities are limited Theory But actions to imitate each other.  Fudenberg and Levine (1998) gives the technical basis for the development of models of this type.

Many philosophers be interested in Binmore (also 1994 1998,  2005A) (**), which shows that the application of game analysis theory can subscribe to imagine Rawlsian justice that do not require the use of assumptions Kant about what agents rational that the desire behind the veil of ignorance about their identities and social roles. (In addition, Binmore progress trips to a wide range of other issues on both the central and peripheral in each of the institutions and the limits of game theory, and these books are de force tour.) and almost everyone will be interested in  Frank (1988)  (**), where it is the use of game theory evolutionary to highlight the basic features of human nature and emotion. Although readers of this also draws criticism from model in Frank  Ross and Dumouchel (2004).

Being a survey of behavioral and experimental applications of game theory in the  Kagel and Roth (1995).Camerer (2003)  (**) is a comprehensive study of this literature (which also brings it even now), and that can not be missed by anyone interested in these issues. Shorter poll confirms the philosophical and methodological criticism is  Samuelson (2005). Philosophical foundations also examine carefully in  GUALA (2005).

And published two volumes of the leading theorists that provide sweeping views from the philosophical foundations of the theory of the game in 2009. This is the  Binmore (2009)  (**)  and Gintis (2009)  (**). Both are indispensable for any new interventions on the subject.

Volume in recent interviews with nine of the ten leading game theorists, survey their views on the motives and constituent subjects, is  Hendricks and Hansen (2007).

There followed the evolution of the recent results in the foundations of game theory is the invention of matches conditioned by the theory of  Stirling (2012). The best way to understand the philosophical importance of this work in light of the considerations that have been made ​​in  Bacharach (2006).

The theory of the dynamics of the game from the sub receive a wonderful person, and can be reached, the discussion in Ainslie (2001). Seminal texts in the science of the nervous economy, with widespread use and the implications for behavioral game theory,  and editing and Burns (2002),  Glimcher 2003  (**),  and Camerer, Weinstein and Prelec (2005).  Ross (2005A)  teaches game theory foundations of the micro economy in general, but especially science and nervous economy, from the standpoint of cognitive science behavioral economics.

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