PRISONER’S DILEMMA (ECONOMICS) (Social Science)

The prisoner’s dilemma is a classic example of an environment in which individuals rationally fail to cooperate even though cooperation would make each person better off. A standard formulation is the following: Two men commit a crime and are arrested. The following possible punishments await them. If both men confess, each will receive five years in prison. If neither man confesses, each will receive three years in prison. If one man confesses and the other does not, the confessor will receive one year in prison whereas the other receives ten.

The two men would receive the lightest sentence if both refused to confess than if neither does so. However, suppose each man is a prisoner in his own separate holding cell, so that it is impossible for the two men to coordinate their behavior. If the prisoners are acting rationally, each will confess. The reason is the following: A person convicted of a crime should confess if it reduces his prison sentence. The complication in each man’s decision is that the consequence of his behavior depends on the behavior of the other man, which he does not know. However, in the prisoner’s dilemma, it turns out that the rational choice for a prisoner is to confess regardless of the behavior of the other prisoner. To see this, if the other prisoner confesses, then confession brings a sentence of five years whereas not confessing brings ten years. If the other prisoner does not confess, then confession brings a sentence of one year whereas not confessing brings three. Thus, confession is a dominant strategy as it is always preferable to the alternative. The two men therefore choose strategies that, although individually rational, are collectively inferior to those they would choose if they could cooperate.


When one considers situations where individuals play a sequence of prisoner’s dilemma games, rational behavior leads to very different outcomes. The reason for this is that for repeated prisoner’s dilemma games, each player will be making a sequence of choices so that the decision to cooperate in one game can depend on the past behavior of the other player. This means that players can reward each other by making choices that depend on the play of their opponent. The existence of noncooperative equilibrium strategies for an infinite repeated prisoner’s dilemma has been shown in many contexts; a classic formulation is explored in Drew Fudenberg and Eric Maskin’s 1986 paper. It is also possible for periods of cooperation to occur in finite sequential games, as described in David Kreps et al.’s 1982 work.

The prisoner’s dilemma is a basic component of any game theory textbook; a particularly insightful treatment may be found in Roger Myerson’s Game Theory (1991). A history that places the prisoner’s dilemma in the context of the development of game theory is William Poundstone’s book Prisoner’s Dilemma (1992).

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