Prisoner's dilemma

3992:, p. 118: "A typical contemporary version of the story goes like this: Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police admit they don't have enough evidence to convict the pair on the principal charge. They plan to sentence both to a year in prison on a lesser charge. Simultaneously, the police offer each prisoner a Faustian bargain. If he testifies against his partner, he will go free while the partner will get three years in prison on the main charge. Oh, yes, there is a catch ... If both prisoners testify against each other, both will be sentenced to two years in jail. The prisoners are given a little time to think this over, but in no case may either learn what the other has decided until he has irrevocably made his decision. Each is informed that the other prisoner is being offered the very same deal. Each prisoner is concerned only with his own welfare—with minimizing his own prison sentence." 3021:

the advertising conducted by Firm A. If both Firm A and Firm B chose to advertise during a given period, then the advertisement from each firm negates the other's, receipts remain constant, and expenses increase due to the cost of advertising. Both firms would benefit from a reduction in advertising. However, should Firm B choose not to advertise, Firm A could benefit greatly by advertising. Nevertheless, the optimal amount of advertising by one firm depends on how much advertising the other undertakes. As the best strategy is dependent on what the other firm chooses there is no dominant strategy, which makes it slightly different from a prisoner's dilemma. The outcome is similar, though, in that both firms would be better off were they to advertise less than in the equilibrium.

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relapses in the future is the worst outcome: in some sense, the discipline and self-sacrifice involved in abstaining today have been "wasted" because the future relapse means that the addict is right back where they started and will have to start over. Relapsing today and tomorrow is a slightly "better" outcome, because while the addict is still addicted, they haven't put the effort in to trying to stop. The final case, where one engages in the addictive behavior today while abstaining tomorrow, has the problem that (as in other prisoner's dilemmas) there is an obvious benefit to defecting "today", but tomorrow one will face the same prisoner's dilemma, and the same obvious benefit will be present then, ultimately leading to an endless string of defections.

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defector gets all the winnings, and the cooperator gets nothing. If both defect, both leave with nothing. Notice that the reward matrix is slightly different from the standard one given above, as the rewards for the "both defect" and the "cooperate while the opponent defects" cases are identical. This makes the "both defect" case a weak equilibrium, compared with being a strict equilibrium in the standard prisoner's dilemma. If a contestant knows that their opponent is going to vote "Foe", then their own choice does not affect their own winnings. In a specific sense,

2197: 3068:, whereby an increase in one state's security (such as increasing its military strength) leads other states to fear for their own security out of fear of offensive action. Consequently, security-increasing measures can lead to tensions, escalation or conflict with one or more other parties, producing an outcome which no party truly desires. The security dilemma is particularly intense in situations when it is hard to distinguish offensive weapons from defensive weapons, and offense has the advantage in any conflict over defense. 972:, and won the contest. The strategy is simply to cooperate on the first iteration of the game; after that, the player does what his or her opponent did on the previous move. Depending on the situation, a slightly better strategy can be "tit for tat with forgiveness": when the opponent defects, on the next move, the player sometimes cooperates anyway, with a small probability (around 1–5%, depending on the lineup of opponents). This allows for occasional recovery from getting trapped in a cycle of defections. 1072:, pointed out the possibility of such strategies winning if multiple entries were allowed, but remarked that Axelrod would most likely not have allowed them if they had been submitted. It also relies on circumventing the rule that no communication is allowed between players, which the Southampton programs arguably did with their preprogrammed "ten-move dance" to recognize one another, reinforcing how valuable communication can be in shifting the balance of the game. 1051:

recognize each other through a series of five to ten moves at the start. Once this recognition was made, one program would always cooperate and the other would always defect, assuring the maximum number of points for the defector. If the program realized that it was playing a non-Southampton player, it would continuously defect in an attempt to minimize the competing program's score. As a result, the 2004 Prisoners' Dilemma Tournament results show

1055:'s strategies in the first three places (and a number of positions towards the bottom), despite having fewer wins and many more losses than the GRIM strategy. The Southampton strategy takes advantage of the fact that multiple entries were allowed in this particular competition and that a team's performance was measured by that of the highest-scoring player (meaning that the use of self-sacrificing players was a form of 7085: 101: 3119:, hypothesized that the tragedy of the commons is oversimplified, with the negative outcome influenced by outside influences. Without complicating pressures, groups communicate and manage the commons among themselves for their mutual benefit, enforcing social norms to preserve the resource and achieve the maximum good for the group, an example of effecting the best-case outcome for prisoner's dilemma. 2995:, fast brain signaling associated with processing different rounds may indicate choices at the next round. Mutual cooperation outcomes entail brain activity changes predictive of how quickly a person will cooperate in kind at the next opportunity; this activity may be linked to basic homeostatic and motivational processes, possibly increasing the likelihood of short-cutting into mutual cooperation. 2157: 1101: 764: 317: 161: 7075: 1005:

one who follows the tit-for-tat strategy, that person is at a slight disadvantage because of the loss on the first turn. In such a population, the optimal strategy is to defect every time. More generally, given a population with a certain percentage of always-defectors with the rest being tit-for-tat players, the optimal strategy depends on the percentage and number of iterations played.

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were defined by Ethan Akin to be those for which the player responds to past mutual cooperation with future cooperation and splits expected payoffs equally if he receives at least the cooperative expected payoff. Among good strategies, the generous (ZD) subset performs well when the population is not too small. If the population is very small, defection strategies tend to dominate.

887:: one might as well defect on the last turn, since the opponent will not have a chance to later retaliate. Therefore, both will defect on the last turn. Thus, the player might as well defect on the second-to-last turn, since the opponent will defect on the last no matter what is done, and so on. The same applies if the game length is unknown but has a known upper limit. 2869:

make a variable contribution to the other player. Le and Boyd found that in such situations, cooperation is much harder to evolve than in the discrete iterated prisoner's dilemma. In a continuous prisoner's dilemma, if a population starts off in a non-cooperative equilibrium, players who are only marginally more cooperative than non-cooperators get little benefit from

6280: 292:: B will either cooperate or defect. If B cooperates, A should defect, because going free is better than serving 1 year. If B defects, A should also defect, because serving 2 years is better than serving 3. So, either way, A should defect since defecting is A's best response regardless of B's strategy. Parallel reasoning will show that B should defect. 1079:, tit-for-tat is not always the absolute winner of any given tournament; more precisely, its long-run results over a series of tournaments outperform its rivals, but this does not mean it is the most successful in the short term. The same applies to tit-for-tat with forgiveness and other optimal strategies. 2934:

unknown. This difference suggests that states will cooperate much less than in a real iterated prisoner's dilemma, so that the probability of avoiding a possible climate catastrophe is much smaller than that suggested by a game-theoretical analysis of the situation using a real iterated prisoner's dilemma.

2843:. The key intuition is that an evolutionarily stable strategy must not only be able to invade another population (which extortionary ZD strategies can do) but must also perform well against other players of the same type (which extortionary ZD players do poorly because they reduce each other's surplus). 1030:

for finding an optimal strategy). The mix of algorithms in the final population generally depends on the mix in the initial population. The introduction of mutation (random variation during reproduction) lessens the dependency on the initial population; empirical experiments with such systems tend to

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prisoners testify against each other, both will be sentenced to two years in jail. The prisoners are given a little time to think this over, but in no case may either learn what the other has decided until he has irrevocably made his decision. Each is informed that the other prisoner is being offered

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The tournament has two rounds. In the first round, each of the top eight strategies were nice, and not one of the bottom seven were nice. In the second round (strategy designers could take into account the results of the first round), all but one of the top fifteen strategies were nice (and that one

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This may better reflect real-world scenarios, the researchers giving the example of two scientists collaborating on a report, both of whom would benefit if the other worked harder. "But when your collaborator doesn't do any work, it's probably better for you to do all the work yourself. You'll still

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with one another. By contrast, in a discrete prisoner's dilemma, tit-for-tat cooperators get a big payoff boost from assorting with one another in a non-cooperative equilibrium, relative to non-cooperators. Since nature arguably offers more opportunities for variable cooperation rather than a strict

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Because of this new rule, this competition also has little theoretical significance when analyzing single-agent strategies as compared to Axelrod's seminal tournament. But it provided a basis for analyzing how to achieve cooperative strategies in multi-agent frameworks, especially in the presence of

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In contrast to the one-time prisoner's dilemma game, the optimal strategy in the iterated prisoner's dilemma depends upon the strategies of likely opponents, and how they will react to defections and cooperation. For example, if a population consists entirely of players who always defect, except for

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has been cited as an example of a prisoner's dilemma. Two competing athletes have the option to use an illegal and/or dangerous drug to boost their performance. If neither athlete takes the drug, then neither gains an advantage. If only one does, then that athlete gains a significant advantage over

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Most work on the iterated prisoner's dilemma has focused on the discrete case, in which players either cooperate or defect, because this model is relatively simple to analyze. However, some researchers have looked at models of the continuous iterated prisoner's dilemma, in which players are able to

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An extension of the iterated prisoner's dilemma is an evolutionary stochastic iterated prisoner's dilemma, in which the relative abundance of particular strategies is allowed to change, with more successful strategies relatively increasing. This process may be accomplished by having less successful

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fixed) in which participants have to choose their strategy repeatedly and remember their previous encounters. Axelrod invited academic colleagues from around the world to devise computer strategies to compete in an iterated prisoner's dilemma tournament. The programs that were entered varied widely

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Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police admit they don't have enough evidence to convict the pair on the principal charge. They plan to sentence both to a year

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A prisoner's dilemma is considered "impure" if a mixed strategy may give better expected payoffs than a pure strategy. This creates the interesting possibility that the moral action from a utilitarian perspective (i.e., aiming at maximizing the good of an action) may require randomization of one's

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was legal in the United States, competing cigarette manufacturers had to decide how much money to spend on advertising. The effectiveness of Firm A's advertising was partially determined by the advertising conducted by Firm B. Likewise, the profit derived from advertising for Firm B is affected by

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While extortionary ZD strategies are not stable in large populations, another ZD class called "generous" strategies is both stable and robust. When the population is not too small, these strategies can supplant any other ZD strategy and even perform well against a broad array of generic strategies

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simulation. In such a simulation, tit-for-tat will almost always come to dominate, though nasty strategies will drift in and out of the population because a tit-for-tat population is penetrable by non-retaliating nice strategies, which in turn are easy prey for the nasty strategies. Dawkins showed

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by Alexander Stewart and Joshua Plotkin in 2013. Generous strategies will cooperate with other cooperative players, and in the face of defection, the generous player loses more utility than its rival. Generous strategies are the intersection of ZD strategies and so-called "good" strategies, which

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Tit-for-tat is a ZD strategy which is "fair", in the sense of not gaining advantage over the other player. But the ZD space also contains strategies that, in the case of two players, can allow one player to unilaterally set the other player's score or alternatively force an evolutionary player to

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The iterated prisoner's dilemma is fundamental to some theories of human cooperation and trust. Assuming that the game effectively models transactions between two people that require trust, cooperative behavior in populations can be modeled by a multi-player iterated version of the game. In 1975,

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Two prisoners are separated into individual rooms and cannot communicate with each other. It is assumed that both prisoners understand the nature of the game, have no loyalty to each other, and will have no opportunity for retribution or reward outside of the game. The normal game is shown below:

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A more general set of games is asymmetric. As in the prisoner's dilemma, the best outcome is cooperation, and there are motives for defection. Unlike the symmetric prisoner's dilemma, though, one player has more to lose and/or more to gain than the other. Some such games have been described as a

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Theory and simulations confirm that beyond a critical population size, ZD extortion loses out in evolutionary competition against more cooperative strategies, and as a result, the average payoff in the population increases when the population is larger. In addition, there are some cases in which

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in 2013. Professor Peter Fröhlich's grading policy scaled final exams according to the highest score, meaning that if everyone received the same score, they would all get an A. Students in Fröhlich's classes organized a boycott of the final exam, ensuring that no one took it. As a result, every

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points out that addiction can be cast as an intertemporal prisoner's dilemma problem between the present and future selves of the addict. In this case, "defecting" means relapsing, where not relapsing both today and in the future is by far the best outcome. The case where one abstains today but

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in England introduced a more successful strategy at the 20th-anniversary iterated prisoner's dilemma competition. It relied on collusion between programs to achieve the highest number of points for a single program. The university submitted 60 programs to the competition, which were designed to

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in the US. On the game show, three pairs of people compete. When a pair is eliminated, they play a game similar to the prisoner's dilemma to determine how the winnings are split. If they both cooperate (Friend), they share the winnings 50–50. If one cooperates and the other defects (Foe), the

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An important difference between climate-change politics and the prisoner's dilemma is uncertainty; the extent and pace at which pollution can change climate is not known. The dilemma faced by governments is therefore different from the prisoner's dilemma in that the payoffs of cooperation are

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in a 1959 paper, rational players repeatedly interacting for indefinitely long games can sustain cooperation. Specifically, a player may be less willing to cooperate if their counterpart did not cooperate many times, which causes disappointment. Conversely, as time elapses, the likelihood of

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In experiments, players getting unequal payoffs in repeated games may seek to maximize profits, but only under the condition that both players receive equal payoffs; this may lead to a stable equilibrium strategy in which the disadvantaged player defects every X game, while the other always

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Critics of realism argue that iteration and extending the shadow of the future are solutions to the prisoner's dilemma. When actors play the prisoner's dilemma once, they have incentives to defect, but when they expect to play it repeatedly, they have greater incentives to cooperate.

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Two people meet and exchange closed bags, with the understanding that one of them contains money, and the other contains a purchase. Either player can choose to honor the deal by putting into his or her bag what he or she agreed, or he or she can defect by handing over an empty

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involving strategic behavior. In casual usage, the label "prisoner's dilemma" may be applied to any situation in which two entities could gain important benefits from cooperating or suffer from failing to do so, but find it difficult or expensive to coordinate their activities.

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emissions. The immediate benefit to any one country from maintaining current behavior is perceived to be greater than the purported eventual benefit to that country if all countries' behavior was changed, therefore explaining the impasse concerning climate-change in 2007.

3923:, who always dealt honourably with their business partners (rather than defecting and reneging on promises – a phenomenon that had discouraged earlier long-term unenforceable overseas contracts). It is argued that dealings with reliable merchants allowed the 3144:

student received an A, successfully solving the prisoner's dilemma in a mutually optimal way without iteration. These examples highlight how the prisoner's dilemma can be used to explore cooperative behavior and strategic decision-making in educational contexts.

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may be viewed as an example of a multi-player generalization of the prisoner's dilemma: each villager makes a choice for personal gain or restraint. The collective reward for unanimous or frequent defection is very low payoffs and the destruction of the commons.

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trilogy in a "dilemma prison". The main theme of the series has been described as the "inadequacy of a binary universe" and the ultimate antagonist is a character called the All-Defector. The first book in the series was published in 2010, with the two sequels,

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In coordination games, players must coordinate their strategies for a good outcome. An example is two cars that abruptly meet in a blizzard; each must choose whether to swerve left or right. If both swerve left, or both right, the cars do not collide. The local

3389:, each of whom is given the option of shoveling snow to clear a path or remaining in their car. A player's highest payoff comes from leaving the opponent to clear all the snow by themselves, but the opponent is still nominally rewarded for their work. 3024:

Sometimes cooperative behaviors do emerge in business situations. For instance, cigarette manufacturers endorsed the making of laws banning cigarette advertising, understanding that this would reduce costs and increase profits across the industry.

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The structure of the traditional prisoner's dilemma can be generalized from its original prisoner setting. Suppose that the two players are represented by the colors red and blue and that each player chooses to either "cooperate" or "defect".

982:: The strategy will not be the first to defect (this is sometimes referred to as an "optimistic" algorithm), i.e., it will not "cheat" on its opponent for purely self-interested reasons first. Almost all the top-scoring strategies were nice. 3052:

the competitor, reduced by the legal and/or medical dangers of having taken the drug. But if both athletes take the drug, the benefits cancel out and only the dangers remain, putting them both in a worse position than if neither had doped.

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suggested that people often find problems such as the prisoner's dilemma problem easier to understand when it is illustrated in the form of a simple game, or trade-off. One of several examples he used was "closed bag exchange":

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The prisoner's dilemma has been used in various academic settings to illustrate the complexities of cooperation and competition. One notable example is the classroom experiment conducted by sociology professor Dan Chambliss at

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series has been analyzed by a team of economists, who found that cooperation was "surprisingly high" for amounts of money that would seem consequential in the real world but were comparatively low in the context of the game.

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cooperation tends to rise, owing to the establishment of a "tacit agreement" among participating players. In experimental situations, cooperation can occur even when both participants know how many iterations will be played.

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dichotomy of cooperation or defection, the continuous prisoner's dilemma may help explain why real-life examples of tit-for-tat-like cooperation are extremely rare even though tit-for-tat seems robust in theoretical models.

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achieve a payoff some percentage lower than his own. The extorted player could defect, but would thereby hurt himself by getting a lower payoff. Thus, extortion solutions turn the iterated prisoner's dilemma into a sort of

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If two players play the prisoner's dilemma more than once in succession, remember their opponent's previous actions, and are allowed to change their strategy accordingly, the game is called the iterated prisoner's dilemma.

3704:, are not easily repeated more than once. Moreover, in many situations, the previous rounds' outcomes are unknown to the players, since they are not necessarily the same (e.g. interaction with a panhandler on the street). 994:: Successful strategies must be forgiving. Though players will retaliate, they will cooperate again if the opponent does not continue to defect. This can stop long runs of revenge and counter-revenge, maximizing points. 3385:. In this model, the risk of being exploited through defection is lower, and individuals always gain from taking the cooperative choice. The snowdrift game imagines two drivers who are stuck on opposite sides of a 1039:, faced with a failure to cooperate, the player switches strategy the next turn. In certain circumstances, Pavlov beats all other strategies by giving preferential treatment to co-players using a similar strategy. 3684:

rigs two ferries, one containing prisoners and the other containing civilians, arming both groups with the means to detonate the bomb on each other's ferries, threatening to detonate them both if they hesitate.

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Axelrod discovered that when these encounters were repeated over a long period of time with many players, each with different strategies, greedy strategies tended to do very poorly in the long run while more

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in the 1980s. Starting in 1981, Chambliss proposed that if no student took the final exam, everyone would receive an A, but if even one student took it, those who didn't would receive a zero. In 1988,

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players imitate the more successful strategies, or by eliminating less successful players from the game, while multiplying the more successful ones. It has been shown that unfair ZD strategies are not

2664: 3064:, the prisoner's dilemma is often used to demonstrate why cooperation fails in situations when cooperation between states is collectively optimal but individually suboptimal. A classic example is the 1817:

will be identical, giving the long-term equilibrium result probabilities of the iterated prisoner's dilemma without the need to explicitly evaluate a large number of interactions. It can be seen that

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strategies did better, as judged purely by self-interest. He used this to show a possible mechanism for the evolution of altruistic behavior from mechanisms that are initially purely selfish, by

2722: 1507: 1263: 2800: 1392:. It has been shown that for any memory-n strategy there is a corresponding memory-1 strategy that gives the same statistical results, so that only memory-1 strategies need be considered. 4749:

Hammerstein, P. (2003). Why is reciprocity so rare in social animals? A protestant appeal. In: P. Hammerstein, Editor, Genetic and Cultural Evolution of Cooperation, MIT Press. pp. 83–94.

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If the iterated prisoner's dilemma is played a finite number of times and both players know this, then the dominant strategy and Nash equilibrium is to defect in all rounds. The proof is

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suggests that these views may be reconciled by considering that moral behavior can modify the payoff matrix of a game, transforming it from a prisoner's dilemma into other games.

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that tested what strategies real-life subjects used in iterated prisoner's dilemma situations with perfect monitoring, the majority of chosen strategies were always to defect,

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defecting. If each of the probabilities are either 1 or 0, the strategy is called deterministic. An example of a deterministic strategy is the tit-for-tat strategy written as

653: 5158: 2398: 3136:, a first-year student, successfully organized his classmates to boycott the exam, demonstrating a practical application of game theory and the prisoner's dilemma concept. 2582: 1390: 1332: 2212:

published a new class of strategies for the stochastic iterated prisoner's dilemma called "zero-determinant" (ZD) strategies. The long term payoffs for encounters between

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Cooper, Russell; DeJong, Douglas V.; Forsythe, Robert; Ross, Thomas W. (1996). "Cooperation without Reputation: Experimental Evidence from Prisoner's Dilemma Games".

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Cooperative behavior of many animals can be understood as an example of the iterated prisoner's dilemma. Often animals engage in long-term partnerships; for example,

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to emerge between rational players, the number of rounds must be unknown or infinite. In that case, "always defect" may no longer be a dominant strategy. As shown by

746: 716: 686: 1846: 1752: 3647:, the main characters start by playing a version of the game and escaping from the "prison" altogether. Later, they become actual prisoners and escape once again. 2991:

defines good relationships as those where partners know not to enter into mutual defection behavior, or at least not to get dynamically stuck there in a loop. In

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Regardless of what the other decides, each prisoner gets a higher reward by betraying the other ("defecting"). The reasoning involves analyzing both players'

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Wu, Jiadong; Zhao, Chengye (2019), Sun, Xiaoming; He, Kun; Chen, Xiaoyun (eds.), "Cooperation on the Monte Carlo Rule: Prisoner's Dilemma Game on the Grid",

124:. If he testifies against his partner, he will go free while the partner will get three years in prison on the main charge. Oh, yes, there is a catch ... If 3661:

subarc, the player characters are twice presented with the prisoner's dilemma during their time in two liches' domain, once cooperating and once defecting.

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Several software packages have been created to run simulations and tournaments of the prisoner's dilemma, some of which have their source code available:

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Defection always results in a better payoff than cooperation, so it is a strictly dominant strategy for both players. Mutual defection is the only strong

6521: 4780: 3116: 5703: 3107:, in a book about the prisoner's dilemma, describes a situation in New Zealand where newspaper boxes are left unlocked. It is possible for people to 2200:

The relationship between zero-determinant (ZD), cooperating and defecting strategies in the iterated prisoner's dilemma (iterated prisoner's dilemma)

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in the game. Since the collectively ideal result of mutual cooperation is irrational from a self-interested standpoint, this Nash equilibrium is not

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In a stochastic iterated prisoner's dilemma game, strategies are specified in terms of "cooperation probabilities". In an encounter between player

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Many instances of human interaction and natural processes have payoff matrices like the prisoner's dilemma's. It is therefore of interest to the

68:, each of whom can cooperate for mutual benefit or betray their partner ("defect") for individual reward. This dilemma was originally framed by 781: 334: 178: 31: 7121: 5629: 5530: 5373: 5068: 4882: 4309: 4108: 3927:

for cooperation to spread to other traders, who spread it further until a high degree of cooperation became a profitable strategy in general

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are social animals that engage in reciprocal food exchange. Applying the payoffs from the prisoner's dilemma can help explain this behavior.

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Gokhale CS, Traulsen A. Evolutionary games in the multiverse. Proceedings of the National Academy of Sciences. 2010 Mar 23. 107(12):5500–04.

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Thomas Osang and Arundhati Nandy provide a theoretical explanation with proofs for a regulation-driven win-win situation along the lines of

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Both the one-shot and the iterated prisoner's dilemma have applications in moral philosophy. Indeed, many of the moral situations, such as

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have suggested that the "Iterated Snowdrift Game" may more closely reflect real-world social situations, although this model is actually a

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international relations theorists to demonstrate the why all states (regardless of their internal policies or professed ideology) under

7837: 7372: 7170: 6730: 6327: 4064: 3111:(defecting), but very few do, feeling that if they do not pay then neither will others, destroying the system. Subsequent research by 6239: 2906:. Many natural processes have been abstracted into models in which living beings are engaged in endless games of prisoner's dilemma. 7656: 7475: 6699: 6536: 6314: 6089: 6021: 5400: 3076: 3072: 803: 356: 200: 6461: 5823: 1020:: If the statistical distribution of opposing strategies can be determined an optimal counter-strategy can be derived analytically. 2835:

to a particular value, the range of possibilities is much smaller, consisting only of complete cooperation or complete defection.

7277: 6955: 6319: 5547: 3887:(also called Friedman), which is never first to defect, but once the other defects even once, grim trigger defects from then on. 2587: 7746: 6284: 3853: 2167: 1111: 6359: 3157: 1026:

simulations of populations have been made, where individuals with low scores die off, and those with high scores reproduce (a

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can be expressed as the determinant of a matrix which is a function of the two strategies and the short term payoff vectors:

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Kümmerli, Rolf; Colliard, Caroline; Fiechter, Nicolas; Petitpierre, Blaise; Russier, Flavien; Keller, Laurent (2007-09-25).

4900:"Neural processing of iterated prisoner's dilemma outcomes indicates next-round choice and speed to reciprocate cooperation" 3803: 3786: 3718:

argued that the prisoner's dilemma does not accurately describe the game played by humanity, which he argues is closer to a

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estimated the count of scholarly articles devoted to it at over 2,000. The iterated prisoner's dilemma is also called the "

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encounters, it is called a "memory-n" strategy. A memory-1 strategy is then specified by four cooperation probabilities:

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later formalized the game by structuring the rewards in terms of prison sentences and named it the "prisoner's dilemma".

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Winston Duarte explains the prisoner's dilemma to his 14-year-old daughter, Teresa, to train her in strategic thinking.

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that here, no static mix of strategies forms a stable equilibrium, and the system will always oscillate between bounds.

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as an illustration of the potential tension between the benefit of the individual and the benefit of the community.

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After analyzing the top-scoring strategies, Axelrod stated several conditions necessary for a strategy to succeed:

42: 6792: 6607: 4334:"Human cooperation in the simultaneous and the alternating Prisoner's Dilemma: Pavlov versus Generous Tit-for-Tat" 2922:. It is argued all countries will benefit from a stable climate, but any single country is often hesitant to curb 8193: 8117: 8040: 7776: 7332: 7257: 7114: 6767: 3040:

authorities want potential cartel members to mutually defect, ensuring the lowest possible prices for consumers.

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the very same deal. Each prisoner is concerned only with his own welfare—with minimizing his own prison sentence.

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extortioners may even catalyze cooperation by helping to break out of a face-off between uniform defectors and

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Some game theorists have criticized the use of the prisoner's dilemma as a thinking tool in moral philosophy.

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and to be a prisoner's dilemma game in the strong sense, the following condition must hold for the payoffs:

327: 171: 38: 8071: 6039: 8162: 8142: 8122: 7741: 7646: 7505: 7455: 7450: 7382: 7352: 7272: 7200: 6892: 6782: 5711: 3843: 3374: 3096: 3061: 2992: 1782:

will converge to a matrix with fixed values, giving the long-term probabilities of an encounter producing

1047: 884: 6065:. Annals of Mathematics Study. Vol. 40. Princeton NJ: Princeton University Press. pp. 287–324. 4296:, Communications in Computer and Information Science, vol. 1069, Springer Singapore, pp. 3–15, 143:

If A remains silent but B testifies against A, A will serve three years in prison and B will be set free.

7180: 6933: 6877: 6762: 6597: 6491: 4939: 4088: 3017: 2915: 2284: 2223: 2092: 2046: 1036: 46: 7621: 7035: 7010: 7005: 6857: 3848: 2855:

for iterated prisoner's dilemma, including win–stay, lose–switch. This was proven specifically for the

1970: 1913: 140:

If A testifies against B but B remains silent, A will be set free while B serves three years in prison.

4395: 3032:

are also involved in a (multi-player) prisoner's dilemma. "Cooperating" typically means agreeing to a

2953:

inspect predators cooperatively in groups, and they are thought to punish non-cooperative inspectors.

620: 7955: 7940: 7827: 7822: 7726: 7711: 7676: 7641: 7240: 7185: 7107: 7055: 7040: 7030: 6995: 6943: 6872: 6787: 6659: 6654: 6577: 6572: 6501: 6369: 5429: 4759: 4716: 4691: 4633: 4569: 4502: 4433: 4345: 3911: 2972: 2903: 4481:"Evolutionary instability of Zero Determinant strategies demonstrates that winning isn't everything" 2349: 859:, to prevent alternating cooperation and defection giving a greater reward than mutual cooperation. 8112: 7731: 7681: 7518: 7445: 7425: 7282: 7165: 6817: 6777: 6741: 6674: 6541: 6511: 6506: 6476: 6441: 6436: 5866:"The Dark Knight: Game Theory : Networks Course blog for INFO 2040/CS 2850/Econ 2040/SOC 2090" 4898:

Cervantes Constantino, Garat, Nicolaisen, Paz, Martínez-Montes, Kessel, Cabana, and Gradin (2020).

4679:

Akin, Ethan (2013). "Stable Cooperative Solutions for the Iterated Prisoner's Dilemma". p. 9.

4271: 3818: 3644: 3561: 2537: 2173: 1345: 1287: 1117: 8091: 7950: 7781: 7761: 7611: 7490: 7395: 7322: 7267: 7088: 7045: 7025: 6965: 6938: 6736: 6689: 6679: 6592: 6456: 6398: 6309: 6259: 6098: 5676: 5619: 5611: 5344: 5336: 5274: 5266: 5204: 5196: 5139: 4992: 4984: 4927: 4695: 4680: 4559: 4492: 4315: 4185: 3838: 3828: 3776: 3771: 3652: 3609: 3520: 3165: 3104: 2870: 1878: 1851: 1793: 1665: 1023: 108: 6990: 6637: 6632: 6622: 6587: 6496: 5727:"Human cooperation in social dilemmas: comparing the Snowdrift game with the Prisoner's Dilemma" 5646: 1690: 690:

implies that mutual cooperation is superior to mutual defection, while the payoff relationships

17: 3622:

A game modeled after the iterated prisoner's dilemma is a central focus of the 2012 video game

1276:

will cooperate in the present encounter given that the previous encounter was characterized by

825: 8183: 8076: 8045: 8000: 7895: 7766: 7721: 7696: 7626: 7500: 7430: 7420: 7312: 7262: 7210: 7078: 7060: 7000: 6980: 6970: 6897: 6882: 6802: 6797: 6627: 6582: 6451: 6333: 6323: 6085: 6017: 5989: 5950: 5906: 5764: 5746: 5688: 5684: 5625: 5526: 5453: 5445: 5396: 5369: 5328: 5258: 5188: 5131: 5064: 5041: 4976: 4919: 4878: 4732: 4661: 4597: 4528: 4461: 4373: 4305: 4177: 4104: 4060: 4035: 3896:

For example see the 2003 study for discussion of the concept and whether it can apply in real

3813: 3719: 3666: 3602: 3502: 3191: 1673: 1027: 950: 4275: 8157: 8152: 8086: 8050: 8030: 7990: 7960: 7915: 7870: 7855: 7812: 7666: 7307: 7244: 7230: 7195: 7020: 6985: 6960: 6912: 6837: 6812: 6807: 6719: 6709: 6684: 6251: 6210: 6200: 6149: 5981: 5942: 5898: 5754: 5738: 5666: 5658: 5518: 5437: 5320: 5248: 5240: 5178: 5170: 5123: 5031: 5023: 4968: 4911: 4838: 4724: 4707:

Le S, Boyd R (2007). "Evolutionary Dynamics of the Continuous Iterated Prisoner's Dilemma".

4651: 4641: 4587: 4577: 4518: 4510: 4451: 4441: 4363: 4353: 4297: 4169: 4138: 4096: 4027: 3833: 3694: 3615: 3129: 3065: 3005: 2205: 1076: 1068: 725: 695: 665: 497: 300: 296: 121: 81: 77: 6305: 6070: 1824: 1730: 8055: 8015: 7970: 7885: 7880: 7601: 7553: 7440: 7205: 7175: 7145: 6928: 6907: 6902: 6862: 6704: 6694: 6531: 6526: 6516: 6481: 6223: 6066: 4157: 3808: 3751: 3715: 3676: 3597: 3048: 965: 864: 453:. Similarly, if Blue cooperates while Red defects, then Blue receives the sucker's payoff 7920: 5902: 4420:"Iterated Prisoner's Dilemma contains strategies that dominate any evolutionary opponent" 3079:

will struggle to cooperate with one another even when all benefit from such cooperation.

2527:{\displaystyle \alpha s_{x}+\beta s_{y}+\gamma =D(P,Q,\alpha S_{x}+\beta S_{y}+\gamma U)} 5810: 5433: 4720: 4637: 4573: 4506: 4437: 4349: 3540:

co-operates. Such behavior may depend on the experiment's social norms around fairness.

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did in the previous encounter. Another is the win-stay, lose switch strategy written as

7995: 7985: 7975: 7910: 7900: 7890: 7875: 7671: 7651: 7636: 7631: 7591: 7558: 7543: 7538: 7528: 7337: 6867: 6842: 6832: 6827: 6757: 6557: 6446: 6301: 6162: 5759: 5726: 5036: 5027: 5011: 4656: 4619: 4592: 4547: 4523: 4480: 4456: 4419: 3781: 3756: 3708: 3308: 3200: 3133: 3092: 2938: 2923: 2919: 2883: 2729: 2403: 1398: 872: 476: 456: 436: 416: 396: 376: 73: 65: 5417: 3951: 1167:

is a function of the outcomes of their previous encounters or some subset thereof. If

1031:

produce tit-for-tat players, but no analytic proof exists that this will always occur.

941:

in algorithmic complexity, initial hostility, capacity for forgiveness, and so forth.

8177: 8035: 8025: 7980: 7965: 7945: 7771: 7716: 7691: 7563: 7533: 7523: 7510: 7415: 7357: 7292: 7225: 6847: 6714: 6562: 6297: 6263: 6169: 6054: 6011: 5886: 5348: 5278: 5208: 5012:"Comprehensive tobacco marketing restrictions: promotion, packaging, price and place" 4996: 4931: 4843: 4826: 4764: 4368: 4333: 4319: 4189: 3337: 3112: 3108: 3009:

of social psychology, and it has been used widely to research various topics such as

2209: 895: 868: 289: 69: 8010: 8005: 7860: 7435: 6644: 6617: 6612: 5842:"The Dark Knight's only redeemable character is the criminal who saves the ferries" 5809:

Beckenkamp, Martin; Hennig-Schmidt, Heike; Maier-Rigaud, Frank P. (March 4, 2007).

5680: 5253: 5183: 4015: 3884: 3823: 3723: 3382: 3360: 3348: 3332: 2988: 911: 6293:

The Prisoner's Dilemma in ornithology – mathematical cartoon by Larry Gonick.

6255: 4915: 4799: 4031: 1906:. Thus, the stationary vector specifies the equilibrium outcome probabilities for 5363: 5063:(8th ed.). Fort Worth, TX: Dryden Press : Harcourt College Publishers. 3016:

Advertising is sometimes cited as a real example of the prisoner's dilemma. When

2941:'s hypothesis, in which government regulation of competing firms is substantial. 413:. If Blue defects while Red cooperates, then Blue receives the temptation payoff 393:

for cooperating. If both players defect, they both receive the punishment payoff

8127: 7930: 7925: 7905: 7701: 7686: 7495: 7465: 7400: 7390: 7220: 7155: 7131: 6822: 6110: 4899: 4301: 3761: 3729: 3033: 2956: 1529:-th entry is the probability that the outcome of a particular encounter between 961: 907: 891: 820:

In addition to the general form above, the iterative version also requires that

763: 316: 160: 100: 61: 6111:"Simulating the evolution of behavior: the iterated prisoners' dilemma problem" 5390: 4972: 4728: 4625:

Proceedings of the National Academy of Sciences of the United States of America

4425:

Proceedings of the National Academy of Sciences of the United States of America

3711:

uses the prisoner's dilemma to show how morality and rationality can conflict.

120:

in prison on a lesser charge. Simultaneously, the police offer each prisoner a

7756: 7410: 6385: 6381: 6344: 6290: 6154: 6137: 5985: 5946: 4100: 3916: 3311: 3037: 1576:

s point of view, the probability that the outcome of the present encounter is

6337: 6177:

Institutions and the Path to the Modern Economy: Lessons from Medieval Trade.

5993: 5954: 5910: 5750: 5522: 5449: 5332: 5262: 5192: 5135: 5086:"Lance Armstrong and the Prisoners' Dilemma of Doping in Professional Sports" 4980: 4181: 4039: 3741:

strategy, such as cooperating with 80% chance and defecting with 20% chance.

2666:

are by definition a ZD strategy, and the long-term payoffs obey the relation

7661: 7581: 7405: 6382:

What The Prisoner's Dilemma Reveals About Life, The Universe, and Everything

6349: 6180: 5783: 5616:

The Prisoner's Dilemma Computer Tournaments and the Evolution of Cooperation

5441: 4646: 4620:"From extortion to generosity, evolution in the Iterated Prisoner's Dilemma" 4582: 4446: 3874:

ranked eighth). Of the bottom fifteen strategies, all but one were not nice.

3792: 3576: 3516: 3386: 3010: 2968: 2895: 2887: 1056: 968:. It was the simplest of any program entered, containing only four lines of 914:. Which strategy the subjects chose depended on the parameters of the game. 5791:. Meetings of the Canadian Economics Association, Toronto, June 4–6, 2004. 5768: 5742: 5662: 5045: 4923: 4781:"Game theory suggests current climate negotiations won't avert catastrophe" 4736: 4665: 4601: 4532: 4465: 4377: 4358: 4142: 3909:

This argument for the development of cooperation through trust is given in

111:

described this "typical contemporary version" of the game in his 1993 book

6279: 6215: 5515:

Governing the Commons: The Evolution of Institutions for Collective Action

5457: 4801:

Environmental Regulation of Polluting Firms: Porter's Hypothesis Revisited

4394:(Press release). University of Southampton. 7 October 2004. Archived from 1664:. Under these definitions, the iterated prisoner's dilemma qualifies as a 8096: 7596: 6375: 4173: 3928: 3897: 3798: 3701: 3588:, a fast agent-based modeling program released in 2018 by Marcos Cardinot 3091:

Many real-life dilemmas involve multiple players. Although metaphorical,

2899: 2891: 1679:

One result of stochastic theory is that there exists a stationary vector

946: 7099: 6138:"The prisoner's dilemma paradox: Rationality, morality, and reciprocity" 2809:

to a specific value within a particular range of values, independent of

7817: 7807: 7485: 6422: 6205: 6188: 5340: 5308: 5270: 5228: 5200: 5143: 4514: 3557: 3320: 1066:

Long before this new-rules tournament was played, Dawkins, in his book

788: in this section. Unsourced material may be challenged and removed. 341: in this section. Unsourced material may be challenged and removed. 185: in this section. Unsourced material may be challenged and removed. 137:

If A and B both remain silent, they will each serve one year in prison.

5704:"'Snowdrift' game tops 'Prisoner's Dilemma' in explaining cooperation" 5671: 5493:"The Volokh Conspiracy " Elinor Ostrom and the Tragedy of the Commons" 4988: 4959:

Axelrod, Robert (1980). "Effective Choice in the Prisoner's Dilemma".

4016:"How to make cooperation the optimizing strategy in a two-person game" 146:

If A and B testify against each other, they will each serve two years.

133:

This leads to four different possible outcomes for prisoners A and B:

5112:""Prisoner's Dilemma" and "Chicken" Models in International Politics" 5111: 4825:

Brosnan, Sarah F.; Earley, Ryan L.; Dugatkin, Lee A. (October 2003).

3029: 1043: 6390: 5324: 5244: 5174: 5127: 4392:"University of Southampton team wins Prisoner's Dilemma competition" 1676:, allowing all of the theory of stochastic processes to be applied. 5591:"Johns Hopkins Students Boycott Final Exam - So Everyone Gets an A" 3556:

run by Robert Axelrod (written by Axelrod and many contributors in

1754:

will give the probability that the outcome of an encounter between

1723:

is normalized so that the sum of its four components is unity. The

7586: 5811:"Cooperation in Symmetric and Asymmetric Prisoner's Dilemma Games" 4685: 4564: 4497: 3533: 3156: 2950: 2195: 969: 99: 4265:"Bayesian Nash equilibrium; a statistical test of the hypothesis" 6486: 5647:"Split or Steal? Cooperative Behavior When the Stakes Are Large" 5621:

Metamagical Themas: questing for the essence of mind and pattern

3924: 3013:

competition and collective action to produce a collective good.

7103: 6394: 6189:"Tit for tat and beyond: the legendary work of Anatol Rapoport" 4158:"Strategy Choice in the Infinitely Repeated Prisoner's Dilemma" 1000:: The strategy must not strive to score more than the opponent. 932:, in which he reports on a tournament that he organized of the 750:

imply that defection is the dominant strategy for both agents.

4546:

Hilbe, Christian; Martin A. Nowak; Karl Sigmund (April 2013).

3693:

The prisoner's dilemma is commonly used as a thinking tool in

2150: 1094: 757: 310: 154: 6167:

The Mathematics of Games of Strategy: Theory and Applications

4548:"Evolution of extortion in Iterated Prisoner's Dilemma games" 4089:"16. Acceptable Points in General Cooperative n-Person Games" 1013:

Deriving the optimal strategy is generally done in two ways:

917: 6240:"Motives for cooperation in the one-shot prisoner's dilemma" 3680:

includes a scene loosely based on the problem in which the

922:

Interest in the iterated prisoner's dilemma was kindled by

3640:

The Mysterious Benedict Society and the Prisoner's Dilemma

2659:{\displaystyle D(P,Q,\alpha S_{x}+\beta S_{y}+\gamma U)=0} 3346:, as well as for the winning couple on the reality shows 373:

If both players cooperate, they both receive the reward

5731:

Proceedings of the Royal Society B: Biological Sciences

4093:

Contributions to the Theory of Games (AM-40), Volume IV

3585: 3199:

has a rewards model between prisoner's dilemma and the

1719:. Without loss of generality, it may be specified that 918:

Axelrod's tournament and successful strategy conditions

6061:-person games". In Luce, R. D.; Tucker, A. W. (eds.). 5548:"A look back at another successful final exam boycott" 5365:

Perception and Misperception in International Politics

3139:

Nearly 25 years later, a similar incident occurred at

5819:

Max Planck Institute for Research on Collective Goods

2742: 2672: 2590: 2540: 2426: 2406: 2352: 2287: 2226: 2095: 2049: 1973: 1916: 1881: 1854: 1827: 1796: 1733: 1693: 1590: 1425: 1415:

is defined as the above 4-element strategy vector of

1401: 1348: 1290: 1181: 828: 728: 698: 668: 623: 479: 459: 439: 419: 399: 379: 8105: 8064: 7846: 7790: 7572: 7474: 7381: 7239: 7138: 6921: 6750: 6550: 6429: 3664:In the 8th novel from the author James S. A. Corey 3190:is a game show that aired from 2002 to 2003 on the 3071:The prisoner's dilemma has frequently been used by 6238:Schneider, Mark; Shields, Timothy W. (June 2022). 6057:(1959). "Acceptable points in general cooperative 5294:Idealist Internationalism and the Security Dilemma 2918:, the dilemma is evident in crises such as global 2794: 2717:{\displaystyle \alpha s_{x}+\beta s_{y}+\gamma =0} 2716: 2658: 2576: 2526: 2412: 2392: 2334: 2273: 2127: 2081: 2016: 1959: 1894: 1867: 1840: 1809: 1746: 1711: 1656: 1501: 1407: 1384: 1326: 1257: 1155:s strategy is specified by a set of probabilities 849: 740: 710: 680: 647: 485: 465: 445: 425: 405: 385: 4798:Osang, Thomas; Nandyyz, Arundhati (August 2003). 4618:Stewart, Alexander J.; Joshua B. Plotkin (2013). 4014:Grofman, Bernard; Pool, Jonathan (January 1977). 2898:, as well as to the biological sciences, such as 1502:{\displaystyle Q=\{Q_{cc},Q_{cd},Q_{dc},Q_{dd}\}} 1258:{\displaystyle P=\{P_{cc},P_{cd},P_{dc},P_{dd}\}} 1082:This can also be illustrated using the Darwinian 5785:Alibi games: the Asymmetric Prisoner' s Dilemmas 4095:, Princeton University Press, pp. 287–324, 4056:Industrial Organization: Theory and Applications 3532:prisoner's dilemma in which one prisoner has an 2856: 6016:(1st Anchor Books ed.). New York: Anchor. 5968:Kuhn, Steven T.; Moresi, Serge (October 1995). 5368:. Princeton University Press. pp. 58–113. 5061:Intermediate microeconomics and its application 4338:Proceedings of the National Academy of Sciences 4263:Landsberger, Michael; Tsirelson, Boris (2003). 4156:Dal Bó, Pedro; Fréchette, Guillaume R. (2019). 4059:. Massachusetts Institute of Technology Press. 3512:convention helps to co-ordinate their actions. 3171: 964:, developed and entered into the tournament by 5416:Axelrod, Robert; Hamilton, William D. (1981). 4613: 4611: 3161:The prisoner's dilemma as a briefcase exchange 2035:s point of view), the equilibrium payoffs for 902:According to a 2019 experimental study in the 7115: 6406: 5782:Robinson, D.R.; Goforth, D.J. (May 5, 2004). 3307:This payoff matrix has also been used on the 3028:Without enforceable agreements, members of a 2795:{\displaystyle D(P,Q,\beta S_{y}+\gamma U)=0} 2342:, which do not involve the stationary vector 2170:to certain ideas, incidents, or controversies 1114:to certain ideas, incidents, or controversies 8: 6193:Negotiation and Conflict Management Research 4944:: CS1 maint: multiple names: authors list ( 4413: 4411: 4409: 4407: 4405: 3619:, published in 2012 and 2014, respectively. 2571: 2547: 2143:to be compared for their long-term payoffs. 2011: 1987: 1954: 1930: 1496: 1432: 1379: 1355: 1321: 1297: 1252: 1188: 1042:Although tit-for-tat is considered the most 433:, while Red receives the "sucker's" payoff, 5309:"The Security Dilemma in Alliance Politics" 4332:Wedekind, C.; Milinski, M. (2 April 1996). 3003:The prisoner's dilemma has been called the 504:Canonical prisoner's dilemma payoff matrix 473:, while Red receives the temptation payoff 104:An example prisoner's dilemma payoff matrix 7122: 7108: 7100: 7074: 6413: 6399: 6391: 6063:Contributions to the Theory 23 of Games IV 5970:"Pure and Utilitarian Prisoner's Dilemmas" 5645:Van den Assem, Martijn J. (January 2012). 5479: 4001: 3989: 3977: 3448:Example prisoner's dilemma payouts (A, B) 2180:this issue before removing this message. 2024:as the short-term payoff vectors for the { 1657:{\displaystyle M_{cd,cd}=P_{cd}(1-Q_{dc})} 1124:this issue before removing this message. 6214: 6204: 6153: 5758: 5670: 5392:Rational Theory of International Politics 5252: 5182: 5035: 4842: 4684: 4655: 4645: 4591: 4581: 4563: 4522: 4496: 4455: 4445: 4367: 4357: 3117:Nobel Memorial Prize in Economic Sciences 2768: 2741: 2696: 2680: 2671: 2632: 2616: 2589: 2539: 2506: 2490: 2450: 2434: 2425: 2405: 2357: 2351: 2323: 2292: 2286: 2262: 2231: 2225: 2119: 2100: 2094: 2073: 2054: 2048: 1978: 1972: 1921: 1915: 1886: 1880: 1859: 1853: 1832: 1826: 1801: 1795: 1738: 1732: 1692: 1642: 1620: 1595: 1589: 1487: 1471: 1455: 1439: 1424: 1400: 1347: 1289: 1243: 1227: 1211: 1195: 1180: 827: 804:Learn how and when to remove this message 727: 697: 667: 622: 478: 458: 438: 418: 398: 378: 357:Learn how and when to remove this message 201:Learn how and when to remove this message 5229:"Cooperation Under the Security Dilemma" 5159:"Cooperation under the Security Dilemma" 3915:, where it is argued that long-distance 3515:Symmetrical co-ordination games include 3446: 3399: 3208: 2816:s strategy, offering an opportunity for 1171:is a function of only their most recent 1075:Even without implicit collusion between 502: 216: 6376:Iterated Prisoner's Dilemma online game 5887:"Reflections on Ethics and Game Theory" 4787:. Society for Science & the Public. 4479:Adami, Christoph; Arend Hintze (2013). 4250: 4238: 4226: 4214: 4202: 3943: 3866: 2736:is able to choose a strategy for which 1517:'s point of view), a transition matrix 88: 6101:(1993). Rationality and Coordination. 4937: 3103:The commons are not always exploited: 2864:Continuous iterated prisoner's dilemma 1580:given that the previous encounter was 1541:given that the previous encounter was 1091:Stochastic iterated prisoner's dilemma 5931:"Gauthier and the Prisoner's Dilemma" 5924: 5922: 5920: 5222: 5220: 5218: 4418:Press, WH; Dyson, FJ (26 June 2012). 4020:The Journal of Mathematical Sociology 3919:was able to form around a nucleus of 1553:are one of the four outcome indices: 64:thought experiment that involves two 7: 3628:and a minor part in its 2016 sequel 1509:as the 4-element strategy vector of 786:adding citations to reliable sources 339:adding citations to reliable sources 183:adding citations to reliable sources 3957:Stanford Encyclopedia of Philosophy 2174:create a more balanced presentation 1118:create a more balanced presentation 151:Strategy for the prisoner's dilemma 87:The prisoner's dilemma models many 32:Prisoner's dilemma (disambiguation) 7171:First-player and second-player win 6731:What the Tortoise Said to Achilles 6187:Kopelman, Shirli (February 2020). 5903:10.1023/B:SYNT.0000035846.91195.cb 5737:(1628). Royal Society: 2965–2970. 5028:10.1136/tobaccocontrol-2011-050416 4961:The Journal of Conflict Resolution 3809:Prisoner's dilemma and cooperation 3736:Pure and impure prisoner's dilemma 3393:end up with a completed project." 2335:{\displaystyle s_{y}=D(P,Q,S_{y})} 2274:{\displaystyle s_{x}=D(P,Q,S_{x})} 2128:{\displaystyle s_{y}=v\cdot S_{y}} 2082:{\displaystyle s_{x}=v\cdot S_{x}} 1887: 1860: 1802: 25: 6372:, an example of the donation game 6315:Concise Encyclopedia of Economics 6109:Chess, David M. (December 1988). 6084:(Revised ed.). Basic Books. 3625:Zero Escape: Virtue's Last Reward 3401:Example snowdrift payouts (A, B) 2346:. Since the determinant function 2017:{\displaystyle S_{y}=\{R,T,S,P\}} 1960:{\displaystyle S_{x}=\{R,S,T,P\}} 76:in 1950 while they worked at the 7278:Coalition-proof Nash equilibrium 7084: 7083: 7073: 6320:Library of Economics and Liberty 6278: 6131:from the original on 2015-05-30. 5829:from the original on 2019-09-02. 5798:from the original on 2004-12-06. 5593:. Baltimore Fishbowl. 2013-02-25 4844:10.1046/j.0179-1613.2003.00928.x 4814:from the original on 2010-07-02. 4087:Aumann, Robert J. (2016-03-02), 2155: 1099: 762: 648:{\displaystyle T>R>P>S} 315: 159: 18:Iterated prisoner's dilemma 6345:Dawkins: Nice Guys Finish First 6136:Collins, Rory W. (March 2022). 5116:International Studies Quarterly 3883:In contrast to strategies like 3536:, hence the term "alibi game". 936:-step prisoner's dilemma (with 773:needs additional citations for 754:The iterated prisoner's dilemma 326:needs additional citations for 170:needs additional citations for 27:Standard example in game theory 7288:Evolutionarily stable strategy 6318:(2nd ed.). Indianapolis: 6226:and Albert M. Chammah (1965). 6142:Think: Philosophy for Everyone 5929:Kuhn, Steven (December 2016). 5885:Kuhn, Steven T. (2004-07-01). 5840:Romain, Lindsey (2018-07-18). 5568:Wolfers, Justin (2013-02-14). 5517:. Cambridge University Press. 5418:"The Evolution of Cooperation" 5395:. Princeton University Press. 5084:Schneier, Bruce (2012-10-26). 5010:Henriksen, Lisa (March 2012). 4877:. Cambridge University Press. 4779:Rehmeyer, Julie (2012-10-29). 4709:Journal of Theoretical Biology 3631:Zero Escape: Zero Time Dilemma 3527:Asymmetric prisoner's dilemmas 3062:international relations theory 2783: 2746: 2647: 2594: 2521: 2468: 2393:{\displaystyle s_{y}=D(P,Q,f)} 2387: 2369: 2329: 2304: 2268: 2243: 2135:, allowing the two strategies 1790:. In other words, the rows of 1651: 1629: 1: 7216:Simultaneous action selection 6256:10.1080/15427560.2022.2081974 6244:Journal of Behavioral Finance 4916:10.1080/17470919.2020.1859410 4032:10.1080/0022250x.1977.9989871 3600:set the opening scene of his 2577:{\displaystyle U=\{1,1,1,1\}} 1385:{\displaystyle P=\{1,0,0,1\}} 1327:{\displaystyle P=\{1,0,1,0\}} 8148:List of games in game theory 7328:Quantal response equilibrium 7318:Perfect Bayesian equilibrium 7253:Bayes correlated equilibrium 6352:Iterated Prisoner's Dilemma 6232:University of Michigan Press 6179:Cambridge University Press, 6081:The Evolution of Cooperation 6010:Poundstone, William (1993). 4294:Theoretical Computer Science 3854:Unscrupulous diner's dilemma 3510:left- and right-hand traffic 3206:This is the rewards matrix: 2584:). Any strategies for which 1513:(where the indices are from 1046:basic strategy, a team from 929:The Evolution of Cooperation 8219:Inefficiency in game theory 7617:Optional prisoner's dilemma 7348:Self-confirming equilibrium 6360:Play Prisoner's Dilemma on 5389:Glaser, Charles L. (2010). 4302:10.1007/978-981-15-0105-0_1 4131:Games and Economic Behavior 3804:Optional prisoner's dilemma 3787:Innocent prisoner's dilemma 3109:take a paper without paying 2147:Zero-determinant strategies 1895:{\displaystyle M^{\infty }} 1868:{\displaystyle M^{\infty }} 1821:is a stationary vector for 1810:{\displaystyle M^{\infty }} 51:Innocent prisoner's dilemma 8235: 8209:Social science experiments 8082:Principal variation search 7798:Aumann's agreement theorem 7461:Strategy-stealing argument 7373:Trembling hand equilibrium 7303:Markov perfect equilibrium 7298:Mertens-stable equilibrium 6103:Cambridge University Press 6048:Cambridge University Press 5059:Nicholson, Walter (2000). 4973:10.1177/002200278002400101 4862:. Oxford University Press. 4729:10.1016/j.jtbi.2006.09.016 3767:Folk theorem (game theory) 3500: 1712:{\displaystyle v\cdot M=v} 43:Unexpected hanging paradox 36: 29: 8118:Combinatorial game theory 7777:Princess and monster game 7333:Quasi-perfect equilibrium 7258:Bayesian Nash equilibrium 7069: 6155:10.1017/S1477175621000464 5986:10.1017/S0266267100003424 5947:10.1017/S0012217316000603 5702:Zyga, Lisa (2007-10-09). 5624:. Bantam Dell Pub Group. 5546:Rivard, Ry (2013-02-21). 5307:Snyder, Glenn H. (1984). 5110:Snyder, Glenn H. (1971). 4858:Dawkins, Richard (1976). 4101:10.1515/9781400882168-018 3726:shares this perspective. 3272: 3239: 3230: 3223: 2824:(and vice versa). But if 1766:given that the encounter 1053:University of Southampton 1018:Bayesian Nash equilibrium 850:{\displaystyle 2R>T+S} 571: 532: 525: 520: 496:This can be expressed in 8133:Evolutionary game theory 7866:Antoine Augustin Cournot 7752:Guess 2/3 of the average 7549:Strictly determined game 7343:Satisfaction equilibrium 7161:Escalation of commitment 6078:Axelrod, Robert (2006). 5974:Economics and Philosophy 5523:10.1017/CBO9781316423936 5513:Ostrom, Elinor (2015) . 5495:. Volokh.com. 2009-10-12 4873:Ainslie, George (2001). 4162:American Economic Review 3900:or strategic situations. 3552:The source code for the 3526: 3141:Johns Hopkins University 2043:can now be specified as 1272:is the probability that 904:American Economic Review 660:The payoff relationship 37:Not to be confused with 8138:Glossary of game theory 7737:Stackelberg competition 7363:Strong Nash equilibrium 6650:Paradoxes of set theory 6291:The Bowerbird's Dilemma 6172:, Englewood Cliffs, NJ. 5442:10.1126/science.7466396 5362:Jervis, Robert (1976). 5254:2027/uc1.31158011478350 5227:Jervis, Robert (1978). 5184:2027/uc1.31158011478350 5157:Jervis, Robert (1978). 4647:10.1073/pnas.1306246110 4583:10.1073/pnas.1214834110 4447:10.1073/pnas.1206569109 3735: 3569:, a library written in 3379:University of Edinburgh 2863: 2802:, unilaterally setting 1090: 1035:In the strategy called 753: 249:Prisoner A stays silent 229:Prisoner B stays silent 150: 39:Three prisoners problem 8163:Tragedy of the commons 8143:List of game theorists 8123:Confrontation analysis 7833:Sprague–Grundy theorem 7353:Sequential equilibrium 7273:Correlated equilibrium 5743:10.1098/rspb.2007.0793 5663:10.1287/mnsc.1110.1413 5612:Hofstadter, Douglas R. 5292:Herz, John H. (1950). 4359:10.1073/pnas.93.7.2686 4143:10.1006/game.1996.0013 3844:Tragedy of the commons 3573:, last updated in 1998 3375:University of Lausanne 3176: 3162: 3097:tragedy of the commons 3056:International politics 2993:cognitive neuroscience 2796: 2718: 2660: 2578: 2528: 2414: 2394: 2336: 2275: 2201: 2129: 2083: 2018: 1961: 1896: 1875:, so that each row of 1869: 1842: 1811: 1748: 1713: 1658: 1503: 1409: 1386: 1328: 1259: 1048:Southampton University 851: 742: 741:{\displaystyle P>S} 712: 711:{\displaystyle T>R} 682: 681:{\displaystyle R>P} 649: 487: 467: 447: 427: 407: 387: 263:Prisoner B: goes free 131: 105: 8199:Non-cooperative games 8189:Environmental studies 7936:Jean-François Mertens 6050:, NY, pp. 24–61. 4485:Nature Communications 3373:Researchers from the 3358:. Game data from the 3160: 3115:, winner of the 2009 3077:international anarchy 3018:cigarette advertising 2916:environmental studies 2910:Environmental studies 2849:win–stay, lose–switch 2841:evolutionarily stable 2797: 2719: 2661: 2579: 2529: 2415: 2395: 2337: 2276: 2199: 2130: 2084: 2019: 1962: 1897: 1870: 1843: 1841:{\displaystyle M^{n}} 1812: 1778:approaches infinity, 1749: 1747:{\displaystyle M^{n}} 1714: 1659: 1504: 1410: 1387: 1329: 1260: 1037:win-stay, lose-switch 852: 743: 713: 683: 650: 488: 468: 448: 428: 408: 388: 277:Prisoner A: goes free 117: 103: 89:real-world situations 47:100 prisoners problem 8065:Search optimizations 7941:Jennifer Tour Chayes 7828:Revelation principle 7823:Purification theorem 7762:Nash bargaining game 7727:Bertrand competition 7712:El Farol Bar problem 7677:Electronic mail game 7642:Lewis signaling game 7186:Hierarchy of beliefs 7016:Kavka's toxin puzzle 6788:Income and fertility 6306:"Prisoner's Dilemma" 6287:at Wikimedia Commons 6040:"Prisoner's Dilemma" 5572:. The New York Times 4760:"Markets & Data" 4174:10.1257/aer.20181480 3952:"Prisoner's Dilemma" 3912:The Wisdom of Crowds 3087:Multiplayer dilemmas 2985:The Science of Trust 2973:behavioral economics 2904:evolutionary biology 2740: 2670: 2588: 2538: 2424: 2404: 2350: 2285: 2224: 2093: 2047: 1971: 1914: 1879: 1852: 1825: 1794: 1731: 1691: 1588: 1569:. For example, from 1423: 1399: 1346: 1288: 1179: 1159:of cooperating with 826: 782:improve this article 726: 696: 666: 621: 477: 457: 437: 417: 397: 377: 335:improve this article 282:Each serves 2 years 268:Prisoner A testifies 238:Prisoner B testifies 179:improve this article 30:For other uses, see 8214:Thought experiments 8113:Bounded rationality 7732:Cournot competition 7682:Rock paper scissors 7657:Battle of the sexes 7647:Volunteer's dilemma 7519:Perfect information 7446:Dominant strategies 7283:Epsilon-equilibrium 7166:Extensive-form game 6675:Temperature paradox 6598:Free choice paradox 6462:Fitch's knowability 6099:Bicchieri, Cristina 6044:Prisoners of Reason 6038:Amadae, S. (2016). 5570:"Gaming the System" 5482:, pp. 126–127. 5434:1981Sci...211.1390A 5428:(4489): 1390–1396. 5296:. pp. 157–180. 4904:Social Neuroscience 4721:2007JThBi.245..258L 4696:2012arXiv1211.0969A 4638:2013PNAS..11015348S 4574:2013PNAS..110.6913H 4507:2013NatCo...4.2193A 4438:2012PNAS..10910409P 4350:1996PNAS...93.2686W 4272:Tel Aviv University 3819:Reciprocal altruism 3689:In moral philosophy 3645:Trenton Lee Stewart 3449: 3402: 3153:Closed-bag exchange 2820:to "extort" player 1521:may be defined for 1077:software strategies 505: 279:Prisoner B: 3 years 261:Prisoner A: 3 years 8092:Paranoid algorithm 8072:Alpha–beta pruning 7951:John Maynard Smith 7782:Rendezvous problem 7622:Traveler's dilemma 7612:Gift-exchange game 7607:Prisoner's dilemma 7524:Large Poisson game 7491:Bargaining problem 7396:Backward induction 7368:Subgame perfection 7323:Proper equilibrium 7051:Prisoner's dilemma 6737:Heat death paradox 6725:Unexpected hanging 6690:Chicken or the egg 6370:Evolution of Trust 6310:David R. Henderson 6285:Prisoner's dilemma 6228:Prisoner's Dilemma 6206:10.1111/ncmr.12172 6175:Greif, A. (2006). 6013:Prisoner's Dilemma 5651:Management Science 5550:. Inside Higher Ed 4515:10.1038/ncomms3193 4241:, pp. 113–114 3980:, pp. 8, 117. 3849:Traveler's dilemma 3839:Swift trust theory 3829:Social preferences 3777:Gift-exchange game 3772:Free-rider problem 3659:The Suffering Game 3653:The Adventure Zone 3610:The Fractal Prince 3521:Bach or Stravinsky 3497:Coordination games 3447: 3400: 3369:Iterated snowdrift 3166:Douglas Hofstadter 3163: 3105:William Poundstone 2878:Real-life examples 2792: 2714: 2656: 2574: 2524: 2420:, it follows that 2410: 2390: 2332: 2271: 2202: 2125: 2079: 2014: 1957: 1892: 1865: 1838: 1807: 1774:. In the limit as 1770:steps previous is 1744: 1709: 1666:stochastic process 1654: 1499: 1405: 1382: 1324: 1255: 847: 738: 708: 678: 645: 503: 483: 463: 443: 423: 403: 383: 258:Each serves 1 year 113:Prisoner's Dilemma 109:William Poundstone 106: 58:prisoner's dilemma 8204:Social psychology 8171: 8170: 8077:Aspiration window 8046:Suzanne Scotchmer 8001:Oskar Morgenstern 7896:Donald B. Gillies 7838:Zermelo's theorem 7767:Induction puzzles 7722:Fair cake-cutting 7697:Public goods game 7627:Coordination game 7501:Intransitive game 7431:Forward induction 7313:Pareto efficiency 7293:Gibbs equilibrium 7263:Berge equilibrium 7211:Simultaneous game 7097: 7096: 6768:Arrow information 6283:Media related to 5631:978-0-465-04566-2 5532:978-1-107-56978-2 5375:978-0-691-10049-4 5070:978-0-030-25916-6 4884:978-0-521-59694-7 4875:Breakdown of Will 4311:978-981-15-0104-3 4168:(11): 3929–3952. 4110:978-1-4008-8216-8 3814:Public goods game 3720:coordination game 3603:The Quantum Thief 3554:second tournament 3503:Coordination game 3494: 3493: 3490: 3489: 3443: 3442: 3305: 3304: 3192:Game Show Network 3123:Academic settings 2413:{\displaystyle f} 2194: 2193: 2172:. Please help to 2164:This section may 2028:} outcomes (from 1902:will be equal to 1848:and particularly 1674:stochastic matrix 1408:{\displaystyle P} 1138: 1137: 1116:. Please help to 1108:This section may 1028:genetic algorithm 951:natural selection 926:in his 1984 book 814: 813: 806: 610: 609: 486:{\displaystyle T} 466:{\displaystyle S} 446:{\displaystyle S} 426:{\displaystyle T} 406:{\displaystyle P} 386:{\displaystyle R} 367: 366: 359: 286: 285: 211: 210: 203: 16:(Redirected from 8226: 8194:Moral psychology 8158:Topological game 8153:No-win situation 8051:Thomas Schelling 8031:Robert B. Wilson 7991:Merrill M. Flood 7961:John von Neumann 7871:Ariel Rubinstein 7856:Albert W. Tucker 7707:War of attrition 7667:Matching pennies 7308:Nash equilibrium 7231:Mechanism design 7196:Normal-form game 7151:Cooperative game 7124: 7117: 7110: 7101: 7087: 7086: 7077: 7076: 6888:Service recovery 6742:Olbers's paradox 6442:Buridan's bridge 6415: 6408: 6401: 6392: 6341: 6282: 6267: 6224:Rapoport, Anatol 6220: 6218: 6208: 6159: 6157: 6132: 6130: 6115: 6095: 6074: 6027: 5998: 5997: 5965: 5959: 5958: 5926: 5915: 5914: 5882: 5876: 5875: 5873: 5872: 5862: 5856: 5855: 5853: 5852: 5837: 5831: 5830: 5828: 5815: 5806: 5800: 5799: 5797: 5790: 5779: 5773: 5772: 5762: 5722: 5716: 5715: 5710:. Archived from 5699: 5693: 5692: 5674: 5642: 5636: 5635: 5608: 5602: 5601: 5599: 5598: 5587: 5581: 5580: 5578: 5577: 5565: 5559: 5558: 5556: 5555: 5543: 5537: 5536: 5510: 5504: 5503: 5501: 5500: 5489: 5483: 5477: 5471: 5468: 5462: 5461: 5413: 5407: 5406: 5386: 5380: 5379: 5359: 5353: 5352: 5304: 5298: 5297: 5289: 5283: 5282: 5256: 5224: 5213: 5212: 5186: 5154: 5148: 5147: 5107: 5101: 5100: 5098: 5097: 5081: 5075: 5074: 5056: 5050: 5049: 5039: 5007: 5001: 5000: 4956: 4950: 4949: 4943: 4935: 4895: 4889: 4888: 4870: 4864: 4863: 4860:The Selfish Gene 4855: 4849: 4848: 4846: 4822: 4816: 4815: 4813: 4806: 4795: 4789: 4788: 4776: 4770: 4769: 4756: 4750: 4747: 4741: 4740: 4704: 4698: 4690: 4688: 4676: 4670: 4669: 4659: 4649: 4632:(38): 15348–53. 4615: 4606: 4605: 4595: 4585: 4567: 4543: 4537: 4536: 4526: 4500: 4476: 4470: 4469: 4459: 4449: 4432:(26): 10409–13. 4415: 4400: 4399: 4388: 4382: 4381: 4371: 4361: 4344:(7): 2686–2689. 4329: 4323: 4322: 4289: 4283: 4282: 4280: 4274:. Archived from 4269: 4260: 4254: 4248: 4242: 4236: 4230: 4224: 4218: 4212: 4206: 4200: 4194: 4193: 4153: 4147: 4146: 4126: 4120: 4119: 4118: 4117: 4084: 4078: 4077: 4075: 4073: 4053:Shy, Oz (1995). 4050: 4044: 4043: 4011: 4005: 3999: 3993: 3987: 3981: 3975: 3969: 3968: 3966: 3964: 3948: 3932: 3907: 3901: 3894: 3888: 3881: 3875: 3871: 3834:Superrationality 3707:The philosopher 3695:moral philosophy 3616:The Causal Angel 3450: 3403: 3396: 3395: 3300: 3295: 3288: 3283: 3277: 3267: 3262: 3255: 3250: 3244: 3235: 3228: 3220: 3215: 3209: 3130:Hamilton College 3066:security dilemma 2815: 2801: 2799: 2798: 2793: 2773: 2772: 2732:. Specifically, 2723: 2721: 2720: 2715: 2701: 2700: 2685: 2684: 2665: 2663: 2662: 2657: 2637: 2636: 2621: 2620: 2583: 2581: 2580: 2575: 2533: 2531: 2530: 2525: 2511: 2510: 2495: 2494: 2455: 2454: 2439: 2438: 2419: 2417: 2416: 2411: 2399: 2397: 2396: 2391: 2362: 2361: 2341: 2339: 2338: 2333: 2328: 2327: 2297: 2296: 2280: 2278: 2277: 2272: 2267: 2266: 2236: 2235: 2206:William H. Press 2189: 2186: 2159: 2158: 2151: 2134: 2132: 2131: 2126: 2124: 2123: 2105: 2104: 2088: 2086: 2085: 2080: 2078: 2077: 2059: 2058: 2034: 2023: 2021: 2020: 2015: 1983: 1982: 1966: 1964: 1963: 1958: 1926: 1925: 1901: 1899: 1898: 1893: 1891: 1890: 1874: 1872: 1871: 1866: 1864: 1863: 1847: 1845: 1844: 1839: 1837: 1836: 1816: 1814: 1813: 1808: 1806: 1805: 1753: 1751: 1750: 1745: 1743: 1742: 1718: 1716: 1715: 1710: 1663: 1661: 1660: 1655: 1650: 1649: 1628: 1627: 1612: 1611: 1575: 1508: 1506: 1505: 1500: 1495: 1494: 1479: 1478: 1463: 1462: 1447: 1446: 1414: 1412: 1411: 1406: 1391: 1389: 1388: 1383: 1333: 1331: 1330: 1325: 1280:cooperating and 1264: 1262: 1261: 1256: 1251: 1250: 1235: 1234: 1219: 1218: 1203: 1202: 1154: 1133: 1130: 1103: 1102: 1095: 1069:The Selfish Gene 1009:Other strategies 879:General strategy 858: 856: 854: 853: 848: 809: 802: 798: 795: 789: 766: 758: 749: 747: 745: 744: 739: 719: 717: 715: 714: 709: 689: 687: 685: 684: 679: 656: 654: 652: 651: 646: 605: 598: 589: 582: 574: 566: 559: 550: 543: 535: 528: 523: 517: 512: 506: 492: 490: 489: 484: 472: 470: 469: 464: 452: 450: 449: 444: 432: 430: 429: 424: 412: 410: 409: 404: 392: 390: 389: 384: 362: 355: 351: 348: 342: 319: 311: 307:Generalized form 301:Pareto efficient 297:Nash equilibrium 217: 206: 199: 195: 192: 186: 163: 155: 122:Faustian bargain 82:Albert W. Tucker 78:RAND Corporation 21: 8234: 8233: 8229: 8228: 8227: 8225: 8224: 8223: 8174: 8173: 8172: 8167: 8101: 8087:max^n algorithm 8060: 8056:William Vickrey 8016:Reinhard Selten 7971:Kenneth Binmore 7886:David K. Levine 7881:Daniel Kahneman 7848: 7842: 7818:Negamax theorem 7808:Minimax theorem 7786: 7747:Diner's dilemma 7602:All-pay auction 7568: 7554:Stochastic game 7506:Mean-field game 7477: 7470: 7441:Markov strategy 7377: 7243: 7235: 7206:Sequential game 7191:Information set 7176:Game complexity 7146:Congestion game 7134: 7128: 7098: 7093: 7065: 6976:Decision-making 6922:Decision theory 6917: 6746: 6670:Hilbert's Hotel 6603:Grelling–Nelson 6546: 6425: 6419: 6330: 6302:Nalebuff, Barry 6296: 6275: 6270: 6237: 6186: 6135: 6128: 6118:Complex Systems 6113: 6108: 6092: 6077: 6053: 6034: 6032:Further reading 6024: 6009: 6006: 6001: 5967: 5966: 5962: 5928: 5927: 5918: 5884: 5883: 5879: 5870: 5868: 5864: 5863: 5859: 5850: 5848: 5839: 5838: 5834: 5826: 5813: 5808: 5807: 5803: 5795: 5788: 5781: 5780: 5776: 5724: 5723: 5719: 5701: 5700: 5696: 5644: 5643: 5639: 5632: 5614:(1985). "Ch.29 5610: 5609: 5605: 5596: 5594: 5589: 5588: 5584: 5575: 5573: 5567: 5566: 5562: 5553: 5551: 5545: 5544: 5540: 5533: 5512: 5511: 5507: 5498: 5496: 5491: 5490: 5486: 5480:Poundstone 1993 5478: 5474: 5469: 5465: 5415: 5414: 5410: 5403: 5388: 5387: 5383: 5376: 5361: 5360: 5356: 5325:10.2307/2010183 5306: 5305: 5301: 5291: 5290: 5286: 5245:10.2307/2009958 5226: 5225: 5216: 5175:10.2307/2009958 5156: 5155: 5151: 5128:10.2307/3013593 5109: 5108: 5104: 5095: 5093: 5083: 5082: 5078: 5071: 5058: 5057: 5053: 5016:Tobacco Control 5009: 5008: 5004: 4958: 4957: 4953: 4936: 4897: 4896: 4892: 4885: 4872: 4871: 4867: 4857: 4856: 4852: 4837:(10): 823–833. 4824: 4823: 4819: 4811: 4804: 4797: 4796: 4792: 4778: 4777: 4773: 4758: 4757: 4753: 4748: 4744: 4706: 4705: 4701: 4678: 4677: 4673: 4617: 4616: 4609: 4558:(17): 6913–18. 4545: 4544: 4540: 4478: 4477: 4473: 4417: 4416: 4403: 4390: 4389: 4385: 4331: 4330: 4326: 4312: 4291: 4290: 4286: 4278: 4267: 4262: 4261: 4257: 4249: 4245: 4237: 4233: 4225: 4221: 4213: 4209: 4201: 4197: 4155: 4154: 4150: 4128: 4127: 4123: 4115: 4113: 4111: 4086: 4085: 4081: 4071: 4069: 4067: 4052: 4051: 4047: 4013: 4012: 4008: 4002:Poundstone 1993 4000: 3996: 3990:Poundstone 1993 3988: 3984: 3978:Poundstone 1993 3976: 3972: 3962: 3960: 3950: 3949: 3945: 3941: 3936: 3935: 3908: 3904: 3895: 3891: 3882: 3878: 3872: 3868: 3863: 3858: 3752:Abilene paradox 3747: 3738: 3716:Kenneth Binmore 3691: 3677:The Dark Knight 3598:Hannu Rajaniemi 3595: 3560:) is available 3546: 3529: 3505: 3499: 3458: 3455: 3411: 3408: 3371: 3301: 3298: 3296: 3293: 3289: 3286: 3284: 3281: 3275: 3273: 3268: 3265: 3263: 3260: 3256: 3253: 3251: 3248: 3242: 3240: 3233: 3231: 3226: 3224: 3221: 3218: 3216: 3213: 3201:game of Chicken 3183: 3155: 3150: 3125: 3089: 3058: 3049:Doping in sport 3046: 3001: 2965: 2947: 2927: 2912: 2884:social sciences 2880: 2866: 2833: 2813: 2807: 2764: 2738: 2737: 2692: 2676: 2668: 2667: 2628: 2612: 2586: 2585: 2536: 2535: 2502: 2486: 2446: 2430: 2422: 2421: 2402: 2401: 2353: 2348: 2347: 2319: 2288: 2283: 2282: 2258: 2227: 2222: 2221: 2190: 2184: 2181: 2160: 2156: 2149: 2115: 2096: 2091: 2090: 2069: 2050: 2045: 2044: 2032: 1974: 1969: 1968: 1917: 1912: 1911: 1882: 1877: 1876: 1855: 1850: 1849: 1828: 1823: 1822: 1797: 1792: 1791: 1786:independent of 1734: 1729: 1728: 1689: 1688: 1683:for the matrix 1638: 1616: 1591: 1586: 1585: 1573: 1483: 1467: 1451: 1435: 1421: 1420: 1397: 1396: 1344: 1343: 1286: 1285: 1270: 1239: 1223: 1207: 1191: 1177: 1176: 1152: 1134: 1128: 1125: 1104: 1100: 1093: 1011: 966:Anatol Rapoport 920: 881: 824: 823: 821: 810: 799: 793: 790: 779: 767: 756: 724: 723: 721: 694: 693: 691: 664: 663: 661: 619: 618: 616: 606: 601: 599: 594: 590: 585: 583: 578: 572: 567: 562: 560: 555: 551: 546: 544: 539: 533: 526: 521: 518: 515: 513: 510: 475: 474: 455: 454: 435: 434: 415: 414: 395: 394: 375: 374: 363: 352: 346: 343: 332: 320: 309: 278: 269: 262: 250: 239: 230: 226: 224: 222: 207: 196: 190: 187: 176: 164: 153: 98: 66:rational agents 54: 35: 28: 23: 22: 15: 12: 11: 5: 8232: 8230: 8222: 8221: 8216: 8211: 8206: 8201: 8196: 8191: 8186: 8176: 8175: 8169: 8168: 8166: 8165: 8160: 8155: 8150: 8145: 8140: 8135: 8130: 8125: 8120: 8115: 8109: 8107: 8103: 8102: 8100: 8099: 8094: 8089: 8084: 8079: 8074: 8068: 8066: 8062: 8061: 8059: 8058: 8053: 8048: 8043: 8038: 8033: 8028: 8023: 8021:Robert Axelrod 8018: 8013: 8008: 8003: 7998: 7996:Olga Bondareva 7993: 7988: 7986:Melvin Dresher 7983: 7978: 7976:Leonid Hurwicz 7973: 7968: 7963: 7958: 7953: 7948: 7943: 7938: 7933: 7928: 7923: 7918: 7913: 7911:Harold W. Kuhn 7908: 7903: 7901:Drew Fudenberg 7898: 7893: 7891:David M. Kreps 7888: 7883: 7878: 7876:Claude Shannon 7873: 7868: 7863: 7858: 7852: 7850: 7844: 7843: 7841: 7840: 7835: 7830: 7825: 7820: 7815: 7813:Nash's theorem 7810: 7805: 7800: 7794: 7792: 7788: 7787: 7785: 7784: 7779: 7774: 7769: 7764: 7759: 7754: 7749: 7744: 7739: 7734: 7729: 7724: 7719: 7714: 7709: 7704: 7699: 7694: 7689: 7684: 7679: 7674: 7672:Ultimatum game 7669: 7664: 7659: 7654: 7652:Dollar auction 7649: 7644: 7639: 7637:Centipede game 7634: 7629: 7624: 7619: 7614: 7609: 7604: 7599: 7594: 7592:Infinite chess 7589: 7584: 7578: 7576: 7570: 7569: 7567: 7566: 7561: 7559:Symmetric game 7556: 7551: 7546: 7544:Signaling game 7541: 7539:Screening game 7536: 7531: 7529:Potential game 7526: 7521: 7516: 7508: 7503: 7498: 7493: 7488: 7482: 7480: 7472: 7471: 7469: 7468: 7463: 7458: 7456:Mixed strategy 7453: 7448: 7443: 7438: 7433: 7428: 7423: 7418: 7413: 7408: 7403: 7398: 7393: 7387: 7385: 7379: 7378: 7376: 7375: 7370: 7365: 7360: 7355: 7350: 7345: 7340: 7338:Risk dominance 7335: 7330: 7325: 7320: 7315: 7310: 7305: 7300: 7295: 7290: 7285: 7280: 7275: 7270: 7265: 7260: 7255: 7249: 7247: 7237: 7236: 7234: 7233: 7228: 7223: 7218: 7213: 7208: 7203: 7198: 7193: 7188: 7183: 7181:Graphical game 7178: 7173: 7168: 7163: 7158: 7153: 7148: 7142: 7140: 7136: 7135: 7129: 7127: 7126: 7119: 7112: 7104: 7095: 7094: 7092: 7091: 7081: 7070: 7067: 7066: 7064: 7063: 7058: 7053: 7048: 7043: 7038: 7033: 7028: 7023: 7018: 7013: 7008: 7003: 6998: 6993: 6988: 6983: 6978: 6973: 6968: 6963: 6958: 6953: 6952: 6951: 6946: 6941: 6931: 6925: 6923: 6919: 6918: 6916: 6915: 6910: 6905: 6900: 6895: 6893:St. Petersburg 6890: 6885: 6880: 6875: 6870: 6865: 6860: 6855: 6850: 6845: 6840: 6835: 6830: 6825: 6820: 6815: 6810: 6805: 6800: 6795: 6790: 6785: 6780: 6775: 6770: 6765: 6760: 6754: 6752: 6748: 6747: 6745: 6744: 6739: 6734: 6727: 6722: 6717: 6712: 6707: 6702: 6697: 6692: 6687: 6682: 6677: 6672: 6667: 6662: 6657: 6652: 6647: 6642: 6641: 6640: 6635: 6630: 6625: 6620: 6610: 6605: 6600: 6595: 6590: 6585: 6580: 6575: 6570: 6565: 6560: 6554: 6552: 6548: 6547: 6545: 6544: 6539: 6534: 6529: 6524: 6522:Rule-following 6519: 6514: 6509: 6504: 6499: 6494: 6489: 6484: 6479: 6474: 6469: 6464: 6459: 6454: 6449: 6447:Dream argument 6444: 6439: 6433: 6431: 6427: 6426: 6420: 6418: 6417: 6410: 6403: 6395: 6389: 6388: 6379: 6378:by Wayne Davis 6373: 6366: 6357: 6347: 6342: 6329:978-0865976658 6328: 6298:Dixit, Avinash 6294: 6288: 6274: 6273:External links 6271: 6269: 6268: 6250:(4): 438–456. 6235: 6221: 6216:2027.42/153763 6184: 6173: 6160: 6133: 6106: 6096: 6090: 6075: 6055:Aumann, Robert 6051: 6035: 6033: 6030: 6029: 6028: 6022: 6005: 6002: 6000: 5999: 5980:(2): 333–343. 5960: 5941:(4): 659–676. 5916: 5877: 5857: 5832: 5801: 5774: 5717: 5714:on 2024-04-11. 5694: 5637: 5630: 5603: 5582: 5560: 5538: 5531: 5505: 5484: 5472: 5463: 5408: 5401: 5381: 5374: 5354: 5319:(4): 461–495. 5313:World Politics 5299: 5284: 5239:(2): 167–214. 5233:World Politics 5214: 5169:(2): 167–214. 5163:World Politics 5149: 5102: 5076: 5069: 5051: 5022:(2): 147–153. 5002: 4951: 4910:(2): 103–120. 4890: 4883: 4865: 4850: 4817: 4790: 4771: 4751: 4742: 4699: 4671: 4607: 4538: 4471: 4401: 4398:on 2014-04-21. 4383: 4324: 4310: 4284: 4281:on 2005-10-02. 4255: 4251:Axelrod (2006) 4243: 4239:Axelrod (2006) 4231: 4227:Axelrod (2006) 4219: 4215:Axelrod (2006) 4207: 4203:Axelrod (2006) 4195: 4148: 4137:(2): 187–218. 4121: 4109: 4079: 4066:978-0262193665 4065: 4045: 4026:(2): 173–186. 4006: 4004:, p. 118. 3994: 3982: 3970: 3942: 3940: 3937: 3934: 3933: 3902: 3889: 3876: 3865: 3864: 3862: 3859: 3857: 3856: 3851: 3846: 3841: 3836: 3831: 3826: 3821: 3816: 3811: 3806: 3801: 3796: 3789: 3784: 3782:Hobbesian trap 3779: 3774: 3769: 3764: 3759: 3757:Centipede game 3754: 3748: 3746: 3743: 3737: 3734: 3709:David Gauthier 3690: 3687: 3674:The 2008 film 3667:Tiamat's Wrath 3594: 3591: 3590: 3589: 3583: 3577:Axelrod-Python 3574: 3564: 3545: 3542: 3528: 3525: 3501:Main article: 3498: 3495: 3492: 3491: 3488: 3487: 3484: 3481: 3477: 3476: 3473: 3470: 3466: 3465: 3462: 3459: 3456: 3453: 3444: 3441: 3440: 3437: 3434: 3430: 3429: 3426: 3423: 3419: 3418: 3415: 3412: 3409: 3406: 3370: 3367: 3303: 3302: 3297: 3292: 3290: 3285: 3280: 3278: 3270: 3269: 3264: 3259: 3257: 3252: 3247: 3245: 3237: 3236: 3229: 3222: 3217: 3212: 3187:Friend or Foe? 3182: 3180:Friend or Foe? 3177: 3154: 3151: 3149: 3146: 3124: 3121: 3093:Garrett Hardin 3088: 3085: 3057: 3054: 3045: 3042: 3000: 2997: 2977:George Ainslie 2964: 2961: 2946: 2943: 2939:Michael Porter 2925: 2920:climate change 2911: 2908: 2879: 2876: 2865: 2862: 2831: 2805: 2791: 2788: 2785: 2782: 2779: 2776: 2771: 2767: 2763: 2760: 2757: 2754: 2751: 2748: 2745: 2730:ultimatum game 2713: 2710: 2707: 2704: 2699: 2695: 2691: 2688: 2683: 2679: 2675: 2655: 2652: 2649: 2646: 2643: 2640: 2635: 2631: 2627: 2624: 2619: 2615: 2611: 2608: 2605: 2602: 2599: 2596: 2593: 2573: 2570: 2567: 2564: 2561: 2558: 2555: 2552: 2549: 2546: 2543: 2523: 2520: 2517: 2514: 2509: 2505: 2501: 2498: 2493: 2489: 2485: 2482: 2479: 2476: 2473: 2470: 2467: 2464: 2461: 2458: 2453: 2449: 2445: 2442: 2437: 2433: 2429: 2409: 2389: 2386: 2383: 2380: 2377: 2374: 2371: 2368: 2365: 2360: 2356: 2331: 2326: 2322: 2318: 2315: 2312: 2309: 2306: 2303: 2300: 2295: 2291: 2270: 2265: 2261: 2257: 2254: 2251: 2248: 2245: 2242: 2239: 2234: 2230: 2192: 2191: 2176:. Discuss and 2163: 2161: 2154: 2148: 2145: 2122: 2118: 2114: 2111: 2108: 2103: 2099: 2076: 2072: 2068: 2065: 2062: 2057: 2053: 2013: 2010: 2007: 2004: 2001: 1998: 1995: 1992: 1989: 1986: 1981: 1977: 1956: 1953: 1950: 1947: 1944: 1941: 1938: 1935: 1932: 1929: 1924: 1920: 1889: 1885: 1862: 1858: 1835: 1831: 1804: 1800: 1741: 1737: 1708: 1705: 1702: 1699: 1696: 1653: 1648: 1645: 1641: 1637: 1634: 1631: 1626: 1623: 1619: 1615: 1610: 1607: 1604: 1601: 1598: 1594: 1498: 1493: 1490: 1486: 1482: 1477: 1474: 1470: 1466: 1461: 1458: 1454: 1450: 1445: 1442: 1438: 1434: 1431: 1428: 1404: 1381: 1378: 1375: 1372: 1369: 1366: 1363: 1360: 1357: 1354: 1351: 1323: 1320: 1317: 1314: 1311: 1308: 1305: 1302: 1299: 1296: 1293: 1268: 1254: 1249: 1246: 1242: 1238: 1233: 1230: 1226: 1222: 1217: 1214: 1210: 1206: 1201: 1198: 1194: 1190: 1187: 1184: 1136: 1135: 1120:. Discuss and 1107: 1105: 1098: 1092: 1089: 1033: 1032: 1021: 1010: 1007: 1002: 1001: 995: 989: 983: 924:Robert Axelrod 919: 916: 880: 877: 873:peace-war game 846: 843: 840: 837: 834: 831: 812: 811: 770: 768: 761: 755: 752: 737: 734: 731: 707: 704: 701: 677: 674: 671: 658: 657: 644: 641: 638: 635: 632: 629: 626: 608: 607: 600: 593: 591: 584: 577: 575: 569: 568: 561: 554: 552: 545: 538: 536: 530: 529: 524: 519: 514: 509: 482: 462: 442: 422: 402: 382: 365: 364: 323: 321: 314: 308: 305: 290:best responses 284: 283: 280: 275: 265: 264: 259: 256: 246: 245: 236: 227: 223: 220: 209: 208: 167: 165: 158: 152: 149: 148: 147: 144: 141: 138: 97: 94: 74:Melvin Dresher 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 8231: 8220: 8217: 8215: 8212: 8210: 8207: 8205: 8202: 8200: 8197: 8195: 8192: 8190: 8187: 8185: 8182: 8181: 8179: 8164: 8161: 8159: 8156: 8154: 8151: 8149: 8146: 8144: 8141: 8139: 8136: 8134: 8131: 8129: 8126: 8124: 8121: 8119: 8116: 8114: 8111: 8110: 8108: 8106:Miscellaneous 8104: 8098: 8095: 8093: 8090: 8088: 8085: 8083: 8080: 8078: 8075: 8073: 8070: 8069: 8067: 8063: 8057: 8054: 8052: 8049: 8047: 8044: 8042: 8041:Samuel Bowles 8039: 8037: 8036:Roger Myerson 8034: 8032: 8029: 8027: 8026:Robert Aumann 8024: 8022: 8019: 8017: 8014: 8012: 8009: 8007: 8004: 8002: 7999: 7997: 7994: 7992: 7989: 7987: 7984: 7982: 7981:Lloyd Shapley 7979: 7977: 7974: 7972: 7969: 7967: 7966:Kenneth Arrow 7964: 7962: 7959: 7957: 7954: 7952: 7949: 7947: 7946:John Harsanyi 7944: 7942: 7939: 7937: 7934: 7932: 7929: 7927: 7924: 7922: 7919: 7917: 7916:Herbert Simon 7914: 7912: 7909: 7907: 7904: 7902: 7899: 7897: 7894: 7892: 7889: 7887: 7884: 7882: 7879: 7877: 7874: 7872: 7869: 7867: 7864: 7862: 7859: 7857: 7854: 7853: 7851: 7845: 7839: 7836: 7834: 7831: 7829: 7826: 7824: 7821: 7819: 7816: 7814: 7811: 7809: 7806: 7804: 7801: 7799: 7796: 7795: 7793: 7789: 7783: 7780: 7778: 7775: 7773: 7770: 7768: 7765: 7763: 7760: 7758: 7755: 7753: 7750: 7748: 7745: 7743: 7740: 7738: 7735: 7733: 7730: 7728: 7725: 7723: 7720: 7718: 7717:Fair division 7715: 7713: 7710: 7708: 7705: 7703: 7700: 7698: 7695: 7693: 7692:Dictator game 7690: 7688: 7685: 7683: 7680: 7678: 7675: 7673: 7670: 7668: 7665: 7663: 7660: 7658: 7655: 7653: 7650: 7648: 7645: 7643: 7640: 7638: 7635: 7633: 7630: 7628: 7625: 7623: 7620: 7618: 7615: 7613: 7610: 7608: 7605: 7603: 7600: 7598: 7595: 7593: 7590: 7588: 7585: 7583: 7580: 7579: 7577: 7575: 7571: 7565: 7564:Zero-sum game 7562: 7560: 7557: 7555: 7552: 7550: 7547: 7545: 7542: 7540: 7537: 7535: 7534:Repeated game 7532: 7530: 7527: 7525: 7522: 7520: 7517: 7515: 7513: 7509: 7507: 7504: 7502: 7499: 7497: 7494: 7492: 7489: 7487: 7484: 7483: 7481: 7479: 7473: 7467: 7464: 7462: 7459: 7457: 7454: 7452: 7451:Pure strategy 7449: 7447: 7444: 7442: 7439: 7437: 7434: 7432: 7429: 7427: 7424: 7422: 7419: 7417: 7416:De-escalation 7414: 7412: 7409: 7407: 7404: 7402: 7399: 7397: 7394: 7392: 7389: 7388: 7386: 7384: 7380: 7374: 7371: 7369: 7366: 7364: 7361: 7359: 7358:Shapley value 7356: 7354: 7351: 7349: 7346: 7344: 7341: 7339: 7336: 7334: 7331: 7329: 7326: 7324: 7321: 7319: 7316: 7314: 7311: 7309: 7306: 7304: 7301: 7299: 7296: 7294: 7291: 7289: 7286: 7284: 7281: 7279: 7276: 7274: 7271: 7269: 7266: 7264: 7261: 7259: 7256: 7254: 7251: 7250: 7248: 7246: 7242: 7238: 7232: 7229: 7227: 7226:Succinct game 7224: 7222: 7219: 7217: 7214: 7212: 7209: 7207: 7204: 7202: 7199: 7197: 7194: 7192: 7189: 7187: 7184: 7182: 7179: 7177: 7174: 7172: 7169: 7167: 7164: 7162: 7159: 7157: 7154: 7152: 7149: 7147: 7144: 7143: 7141: 7137: 7133: 7125: 7120: 7118: 7113: 7111: 7106: 7105: 7102: 7090: 7082: 7080: 7072: 7071: 7068: 7062: 7059: 7057: 7054: 7052: 7049: 7047: 7044: 7042: 7039: 7037: 7034: 7032: 7029: 7027: 7024: 7022: 7021:Morton's fork 7019: 7017: 7014: 7012: 7009: 7007: 7004: 7002: 6999: 6997: 6994: 6992: 6989: 6987: 6984: 6982: 6979: 6977: 6974: 6972: 6969: 6967: 6964: 6962: 6961:Buridan's ass 6959: 6957: 6954: 6950: 6947: 6945: 6942: 6940: 6937: 6936: 6935: 6934:Apportionment 6932: 6930: 6927: 6926: 6924: 6920: 6914: 6911: 6909: 6906: 6904: 6901: 6899: 6896: 6894: 6891: 6889: 6886: 6884: 6881: 6879: 6876: 6874: 6871: 6869: 6866: 6864: 6861: 6859: 6856: 6854: 6851: 6849: 6846: 6844: 6841: 6839: 6836: 6834: 6831: 6829: 6826: 6824: 6821: 6819: 6816: 6814: 6811: 6809: 6806: 6804: 6801: 6799: 6796: 6794: 6793:Downs–Thomson 6791: 6789: 6786: 6784: 6781: 6779: 6776: 6774: 6771: 6769: 6766: 6764: 6761: 6759: 6756: 6755: 6753: 6749: 6743: 6740: 6738: 6735: 6732: 6728: 6726: 6723: 6721: 6718: 6716: 6713: 6711: 6710:Plato's beard 6708: 6706: 6703: 6701: 6698: 6696: 6693: 6691: 6688: 6686: 6683: 6681: 6678: 6676: 6673: 6671: 6668: 6666: 6663: 6661: 6658: 6656: 6653: 6651: 6648: 6646: 6643: 6639: 6636: 6634: 6631: 6629: 6626: 6624: 6621: 6619: 6616: 6615: 6614: 6611: 6609: 6608:Kleene–Rosser 6606: 6604: 6601: 6599: 6596: 6594: 6591: 6589: 6586: 6584: 6581: 6579: 6576: 6574: 6571: 6569: 6566: 6564: 6561: 6559: 6556: 6555: 6553: 6549: 6543: 6540: 6538: 6535: 6533: 6532:Theseus' ship 6530: 6528: 6525: 6523: 6520: 6518: 6515: 6513: 6510: 6508: 6505: 6503: 6500: 6498: 6495: 6493: 6492:Mere addition 6490: 6488: 6485: 6483: 6480: 6478: 6475: 6473: 6470: 6468: 6465: 6463: 6460: 6458: 6455: 6453: 6450: 6448: 6445: 6443: 6440: 6438: 6435: 6434: 6432: 6430:Philosophical 6428: 6424: 6416: 6411: 6409: 6404: 6402: 6397: 6396: 6393: 6387: 6383: 6380: 6377: 6374: 6371: 6368:Nicky Case's 6367: 6365:(N/A 11-5-17) 6364: 6363: 6358: 6355: 6351: 6348: 6346: 6343: 6339: 6335: 6331: 6325: 6321: 6317: 6316: 6311: 6307: 6303: 6299: 6295: 6292: 6289: 6286: 6281: 6277: 6276: 6272: 6265: 6261: 6257: 6253: 6249: 6245: 6241: 6236: 6233: 6229: 6225: 6222: 6217: 6212: 6207: 6202: 6198: 6194: 6190: 6185: 6182: 6178: 6174: 6171: 6170:Prentice-Hall 6168: 6164: 6161: 6156: 6151: 6148:(61): 45–55. 6147: 6143: 6139: 6134: 6127: 6124:(6): 663–70. 6123: 6119: 6112: 6107: 6104: 6100: 6097: 6093: 6091:0-465-00564-0 6087: 6083: 6082: 6076: 6072: 6068: 6064: 6060: 6056: 6052: 6049: 6045: 6041: 6037: 6036: 6031: 6025: 6023:0-385-41580-X 6019: 6015: 6014: 6008: 6007: 6003: 5995: 5991: 5987: 5983: 5979: 5975: 5971: 5964: 5961: 5956: 5952: 5948: 5944: 5940: 5936: 5932: 5925: 5923: 5921: 5917: 5912: 5908: 5904: 5900: 5896: 5892: 5888: 5881: 5878: 5867: 5861: 5858: 5847: 5843: 5836: 5833: 5825: 5821: 5820: 5812: 5805: 5802: 5794: 5787: 5786: 5778: 5775: 5770: 5766: 5761: 5756: 5752: 5748: 5744: 5740: 5736: 5732: 5728: 5721: 5718: 5713: 5709: 5705: 5698: 5695: 5690: 5686: 5682: 5678: 5673: 5668: 5664: 5660: 5656: 5652: 5648: 5641: 5638: 5633: 5627: 5623: 5622: 5617: 5613: 5607: 5604: 5592: 5586: 5583: 5571: 5564: 5561: 5549: 5542: 5539: 5534: 5528: 5524: 5520: 5516: 5509: 5506: 5494: 5488: 5485: 5481: 5476: 5473: 5467: 5464: 5459: 5455: 5451: 5447: 5443: 5439: 5435: 5431: 5427: 5423: 5419: 5412: 5409: 5404: 5402:9780691143729 5398: 5394: 5393: 5385: 5382: 5377: 5371: 5367: 5366: 5358: 5355: 5350: 5346: 5342: 5338: 5334: 5330: 5326: 5322: 5318: 5314: 5310: 5303: 5300: 5295: 5288: 5285: 5280: 5276: 5272: 5268: 5264: 5260: 5255: 5250: 5246: 5242: 5238: 5234: 5230: 5223: 5221: 5219: 5215: 5210: 5206: 5202: 5198: 5194: 5190: 5185: 5180: 5176: 5172: 5168: 5164: 5160: 5153: 5150: 5145: 5141: 5137: 5133: 5129: 5125: 5122:(1): 66–103. 5121: 5117: 5113: 5106: 5103: 5091: 5087: 5080: 5077: 5072: 5066: 5062: 5055: 5052: 5047: 5043: 5038: 5033: 5029: 5025: 5021: 5017: 5013: 5006: 5003: 4998: 4994: 4990: 4986: 4982: 4978: 4974: 4970: 4966: 4962: 4955: 4952: 4947: 4941: 4933: 4929: 4925: 4921: 4917: 4913: 4909: 4905: 4901: 4894: 4891: 4886: 4880: 4876: 4869: 4866: 4861: 4854: 4851: 4845: 4840: 4836: 4832: 4828: 4821: 4818: 4810: 4803: 4802: 4794: 4791: 4786: 4782: 4775: 4772: 4768:. 2007-09-27. 4767: 4766: 4765:The Economist 4761: 4755: 4752: 4746: 4743: 4738: 4734: 4730: 4726: 4722: 4718: 4715:(2): 258–67. 4714: 4710: 4703: 4700: 4697: 4693: 4687: 4682: 4675: 4672: 4667: 4663: 4658: 4653: 4648: 4643: 4639: 4635: 4631: 4627: 4626: 4621: 4614: 4612: 4608: 4603: 4599: 4594: 4589: 4584: 4579: 4575: 4571: 4566: 4561: 4557: 4553: 4549: 4542: 4539: 4534: 4530: 4525: 4520: 4516: 4512: 4508: 4504: 4499: 4494: 4490: 4486: 4482: 4475: 4472: 4467: 4463: 4458: 4453: 4448: 4443: 4439: 4435: 4431: 4427: 4426: 4421: 4414: 4412: 4410: 4408: 4406: 4402: 4397: 4393: 4387: 4384: 4379: 4375: 4370: 4365: 4360: 4355: 4351: 4347: 4343: 4339: 4335: 4328: 4325: 4321: 4317: 4313: 4307: 4303: 4299: 4295: 4288: 4285: 4277: 4273: 4266: 4259: 4256: 4252: 4247: 4244: 4240: 4235: 4232: 4228: 4223: 4220: 4216: 4211: 4208: 4205:, p. 193 4204: 4199: 4196: 4191: 4187: 4183: 4179: 4175: 4171: 4167: 4163: 4159: 4152: 4149: 4144: 4140: 4136: 4132: 4125: 4122: 4112: 4106: 4102: 4098: 4094: 4090: 4083: 4080: 4068: 4062: 4058: 4057: 4049: 4046: 4041: 4037: 4033: 4029: 4025: 4021: 4017: 4010: 4007: 4003: 3998: 3995: 3991: 3986: 3983: 3979: 3974: 3971: 3959: 3958: 3953: 3947: 3944: 3938: 3930: 3926: 3922: 3918: 3914: 3913: 3906: 3903: 3899: 3893: 3890: 3886: 3880: 3877: 3870: 3867: 3860: 3855: 3852: 3850: 3847: 3845: 3842: 3840: 3837: 3835: 3832: 3830: 3827: 3825: 3822: 3820: 3817: 3815: 3812: 3810: 3807: 3805: 3802: 3800: 3797: 3795: 3794: 3790: 3788: 3785: 3783: 3780: 3778: 3775: 3773: 3770: 3768: 3765: 3763: 3760: 3758: 3755: 3753: 3750: 3749: 3744: 3742: 3733: 3731: 3727: 3725: 3721: 3717: 3712: 3710: 3705: 3703: 3698: 3696: 3688: 3686: 3683: 3679: 3678: 3672: 3670: 3668: 3662: 3660: 3656: 3654: 3648: 3646: 3642: 3641: 3635: 3633: 3632: 3627: 3626: 3620: 3618: 3617: 3612: 3611: 3605: 3604: 3599: 3592: 3587: 3584: 3582: 3579:, written in 3578: 3575: 3572: 3568: 3565: 3563: 3559: 3555: 3551: 3550: 3549: 3543: 3541: 3537: 3535: 3524: 3522: 3518: 3513: 3511: 3504: 3496: 3485: 3482: 3479: 3478: 3474: 3471: 3468: 3467: 3463: 3460: 3452: 3451: 3445: 3438: 3435: 3432: 3431: 3427: 3424: 3421: 3420: 3416: 3413: 3405: 3404: 3398: 3397: 3394: 3390: 3388: 3384: 3380: 3376: 3368: 3366: 3363: 3362: 3357: 3356: 3351: 3350: 3345: 3344: 3339: 3336:, and on the 3335: 3334: 3329: 3328: 3323: 3322: 3317: 3313: 3310: 3291: 3279: 3271: 3258: 3246: 3238: 3211: 3210: 3207: 3204: 3202: 3198: 3197:Friend or Foe 3193: 3189: 3188: 3181: 3178: 3175: 3170: 3167: 3159: 3152: 3148:Related games 3147: 3145: 3142: 3137: 3135: 3131: 3122: 3120: 3118: 3114: 3113:Elinor Ostrom 3110: 3106: 3101: 3098: 3094: 3086: 3084: 3080: 3078: 3074: 3069: 3067: 3063: 3055: 3053: 3050: 3043: 3041: 3039: 3035: 3031: 3026: 3022: 3019: 3014: 3012: 3011:oligopolistic 3008: 3007: 2998: 2996: 2994: 2990: 2986: 2981: 2978: 2974: 2971:research and 2970: 2962: 2960: 2958: 2954: 2952: 2944: 2942: 2940: 2935: 2931: 2928: 2921: 2917: 2909: 2907: 2905: 2901: 2897: 2893: 2889: 2885: 2877: 2875: 2872: 2861: 2858: 2857:donation game 2852: 2850: 2844: 2842: 2836: 2834: 2828:tries to set 2827: 2823: 2819: 2812: 2808: 2789: 2786: 2780: 2777: 2774: 2769: 2765: 2761: 2758: 2755: 2752: 2749: 2743: 2735: 2731: 2725: 2711: 2708: 2705: 2702: 2697: 2693: 2689: 2686: 2681: 2677: 2673: 2653: 2650: 2644: 2641: 2638: 2633: 2629: 2625: 2622: 2617: 2613: 2609: 2606: 2603: 2600: 2597: 2591: 2568: 2565: 2562: 2559: 2556: 2553: 2550: 2544: 2541: 2518: 2515: 2512: 2507: 2503: 2499: 2496: 2491: 2487: 2483: 2480: 2477: 2474: 2471: 2465: 2462: 2459: 2456: 2451: 2447: 2443: 2440: 2435: 2431: 2427: 2407: 2400:is linear in 2384: 2381: 2378: 2375: 2372: 2366: 2363: 2358: 2354: 2345: 2324: 2320: 2316: 2313: 2310: 2307: 2301: 2298: 2293: 2289: 2263: 2259: 2255: 2252: 2249: 2246: 2240: 2237: 2232: 2228: 2219: 2215: 2211: 2210:Freeman Dyson 2207: 2198: 2188: 2179: 2175: 2171: 2169: 2162: 2153: 2152: 2146: 2144: 2142: 2138: 2120: 2116: 2112: 2109: 2106: 2101: 2097: 2074: 2070: 2066: 2063: 2060: 2055: 2051: 2042: 2038: 2031: 2027: 2008: 2005: 2002: 1999: 1996: 1993: 1990: 1984: 1979: 1975: 1951: 1948: 1945: 1942: 1939: 1936: 1933: 1927: 1922: 1918: 1909: 1905: 1883: 1856: 1833: 1829: 1820: 1798: 1789: 1785: 1781: 1777: 1773: 1769: 1765: 1761: 1757: 1739: 1735: 1727:-th entry in 1726: 1722: 1706: 1703: 1700: 1697: 1694: 1686: 1682: 1677: 1675: 1671: 1667: 1646: 1643: 1639: 1635: 1632: 1624: 1621: 1617: 1613: 1608: 1605: 1602: 1599: 1596: 1592: 1583: 1579: 1572: 1568: 1564: 1560: 1556: 1552: 1548: 1544: 1540: 1536: 1532: 1528: 1524: 1520: 1516: 1512: 1491: 1488: 1484: 1480: 1475: 1472: 1468: 1464: 1459: 1456: 1452: 1448: 1443: 1440: 1436: 1429: 1426: 1418: 1402: 1393: 1376: 1373: 1370: 1367: 1364: 1361: 1358: 1352: 1349: 1341: 1337: 1318: 1315: 1312: 1309: 1306: 1303: 1300: 1294: 1291: 1283: 1279: 1275: 1271: 1247: 1244: 1240: 1236: 1231: 1228: 1224: 1220: 1215: 1212: 1208: 1204: 1199: 1196: 1192: 1185: 1182: 1174: 1170: 1166: 1162: 1158: 1151: 1147: 1143: 1132: 1123: 1119: 1115: 1113: 1106: 1097: 1096: 1088: 1085: 1080: 1078: 1073: 1071: 1070: 1064: 1060: 1058: 1054: 1049: 1045: 1040: 1038: 1029: 1025: 1022: 1019: 1016: 1015: 1014: 1008: 1006: 999: 996: 993: 990: 987: 984: 981: 978: 977: 976: 973: 971: 967: 963: 960:strategy was 959: 958:deterministic 954: 952: 948: 942: 939: 935: 931: 930: 925: 915: 913: 909: 905: 900: 897: 896:Robert Aumann 893: 888: 886: 878: 876: 874: 870: 866: 860: 844: 841: 838: 835: 832: 829: 818: 808: 805: 797: 794:November 2012 787: 783: 777: 776: 771:This section 769: 765: 760: 759: 751: 735: 732: 729: 705: 702: 699: 675: 672: 669: 642: 639: 636: 633: 630: 627: 624: 615: 614: 613: 604: 597: 592: 588: 581: 576: 570: 565: 558: 553: 549: 542: 537: 531: 508: 507: 501: 499: 494: 480: 460: 440: 420: 400: 380: 371: 361: 358: 350: 340: 336: 330: 329: 324:This section 322: 318: 313: 312: 306: 304: 302: 298: 293: 291: 281: 276: 273: 267: 266: 260: 257: 254: 248: 247: 243: 237: 234: 228: 219: 218: 215: 205: 202: 194: 184: 180: 174: 173: 168:This section 166: 162: 157: 156: 145: 142: 139: 136: 135: 134: 130: 127: 123: 116: 114: 110: 102: 95: 93: 90: 85: 83: 79: 75: 71: 70:Merrill Flood 67: 63: 59: 52: 48: 44: 40: 33: 19: 8011:Peyton Young 8006:Paul Milgrom 7921:Hervé Moulin 7861:Amos Tversky 7803:Folk theorem 7606: 7514:-player game 7511: 7436:Grim trigger 7050: 7041:Preparedness 6873:Productivity 6853:Mandeville's 6645:Opposite Day 6573:Burali-Forti 6568:Bhartrhari's 6361: 6313: 6247: 6243: 6227: 6199:(1): 60–84. 6196: 6192: 6176: 6166: 6145: 6141: 6121: 6117: 6079: 6062: 6058: 6043: 6012: 6004:Bibliography 5977: 5973: 5963: 5938: 5934: 5894: 5890: 5880: 5869:. Retrieved 5860: 5849:. Retrieved 5845: 5835: 5817: 5804: 5784: 5777: 5734: 5730: 5720: 5712:the original 5707: 5697: 5654: 5650: 5640: 5620: 5615: 5606: 5595:. Retrieved 5585: 5574:. Retrieved 5563: 5552:. Retrieved 5541: 5514: 5508: 5497:. Retrieved 5487: 5475: 5466: 5425: 5421: 5411: 5391: 5384: 5364: 5357: 5316: 5312: 5302: 5293: 5287: 5236: 5232: 5166: 5162: 5152: 5119: 5115: 5105: 5094:. Retrieved 5089: 5079: 5060: 5054: 5019: 5015: 5005: 4964: 4960: 4954: 4940:cite journal 4907: 4903: 4893: 4874: 4868: 4859: 4853: 4834: 4830: 4820: 4800: 4793: 4785:Science News 4784: 4774: 4763: 4754: 4745: 4712: 4708: 4702: 4674: 4629: 4623: 4555: 4551: 4541: 4488: 4484: 4474: 4429: 4423: 4396:the original 4386: 4341: 4337: 4327: 4293: 4287: 4276:the original 4258: 4253:, p. 36 4246: 4234: 4222: 4217:, p. 31 4210: 4198: 4165: 4161: 4151: 4134: 4130: 4124: 4114:, retrieved 4092: 4082: 4072:February 27, 4070:. Retrieved 4055: 4048: 4023: 4019: 4009: 3997: 3985: 3973: 3961:. Retrieved 3955: 3946: 3910: 3905: 3892: 3885:grim trigger 3879: 3869: 3824:Rent-seeking 3791: 3739: 3728: 3724:Brian Skyrms 3713: 3706: 3699: 3692: 3675: 3673: 3665: 3663: 3658: 3651: 3649: 3638: 3636: 3629: 3623: 3621: 3614: 3608: 3601: 3596: 3547: 3538: 3530: 3514: 3506: 3391: 3383:chicken game 3372: 3361:Golden Balls 3359: 3353: 3349:Bachelor Pad 3347: 3341: 3333:Golden Balls 3331: 3327:The Bank Job 3325: 3319: 3315: 3306: 3205: 3196: 3185: 3184: 3179: 3172: 3164: 3138: 3126: 3102: 3090: 3081: 3070: 3059: 3047: 3027: 3023: 3015: 3004: 3002: 2989:John Gottman 2984: 2982: 2966: 2957:Vampire bats 2955: 2948: 2936: 2932: 2913: 2881: 2867: 2853: 2845: 2837: 2829: 2825: 2821: 2817: 2810: 2803: 2733: 2726: 2343: 2217: 2213: 2203: 2182: 2168:undue weight 2165: 2140: 2136: 2040: 2036: 2029: 2025: 1907: 1903: 1818: 1787: 1783: 1779: 1775: 1771: 1767: 1763: 1759: 1755: 1724: 1720: 1684: 1680: 1678: 1669: 1584:is equal to 1581: 1577: 1570: 1566: 1562: 1558: 1554: 1550: 1546: 1542: 1538: 1534: 1530: 1526: 1522: 1518: 1514: 1510: 1416: 1394: 1339: 1338:responds as 1335: 1281: 1277: 1273: 1266: 1172: 1168: 1164: 1160: 1156: 1149: 1145: 1141: 1139: 1126: 1112:undue weight 1109: 1081: 1074: 1067: 1065: 1061: 1041: 1034: 1012: 1003: 997: 991: 985: 979: 974: 956:The winning 955: 943: 937: 933: 927: 921: 912:grim trigger 903: 901: 889: 882: 861: 819: 815: 800: 791: 780:Please help 775:verification 772: 659: 611: 602: 595: 586: 579: 563: 556: 547: 540: 495: 372: 368: 353: 347:January 2023 344: 333:Please help 328:verification 325: 294: 287: 271: 252: 241: 232: 212: 197: 191:January 2023 188: 177:Please help 172:verification 169: 132: 125: 118: 112: 107: 86: 57: 55: 8128:Coopetition 7931:Jean Tirole 7926:John Conway 7906:Eric Maskin 7702:Blotto game 7687:Pirate game 7496:Global game 7466:Tit for tat 7401:Bid shading 7391:Appeasement 7241:Equilibrium 7221:Solved game 7156:Determinacy 7139:Definitions 7132:game theory 6971:Condorcet's 6823:Giffen good 6783:Competition 6537:White horse 6512:Omnipotence 6163:Dresher, M. 5897:(1): 1–44. 5657:(1): 2–20. 5092:. 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