Prisoner's Dilemma

Conceptual Overview

As originally developed, the prisoner's dilemma game involved two prisoners who have been apprehended as suspects in a serious crime (armed robbery, say). The prosecutor, however, only has sufficient evidence to convict them of a lesser offense (burglary), so he separately offers each prisoner the following deal: If you confess and testify against the other prisoner, I will let you off free. Faced with this offer, each prisoner must decide whether to confess or to remain silent. The optimal choice, of course, depends on what each expects the other to do, because if both confess, they will be convicted of the more severe crime (though with a discounted sentence). Figure 1 summarizes the payoffs (measured as years in prison) from the various strategies.

If both prisoners remain silent, each receives 1 year in prison for the lesser charge, whereas if both confess, each is convicted of the more serious charge and imprisoned for 5 years. Finally, if one confesses while the other remains silent, the silent one receives the most severe punishment (10 years), while the confessor is let off. It should be evident that the dominant strategy for both prisoners in this game—that is, the strategy that each should choose regardless of what he thinks the other is doing—is to confess. To see why, note first that if prisoner 1 expects prisoner 2 to confess, it is best for him to confess as well because he will receive 5 rather than 10 years. Alternatively, if prisoner 1 expects prisoner 2 to remain silent, it is again best for him to confess because he gets no prison term rather than 1 year. (The same logic applies to prisoner 2, whose payoffs are symmetric.)

Figure 1 Prisoner's Dilemma.

The reason this game is called a dilemma is that the equilibrium outcome where both prisoners confess is not the outcome that produces the lowest combined prison sentence. In particular, note that if both had remained silent, their combined prison term would have been 2 years, compared to 10 years if they both confess. Indeed, it is this conflict between the equilibrium (noncooperative) outcome and the jointly optimal [Page 1304](cooperative) outcome that makes this game so useful for examining a wide range of social, political, and economic situations that involve strategic behavior. For example, the prisoner's dilemma helps to explain why cartels have such a hard time maintaining a monopoly price, why purely voluntary contributions to a public good tend to result in underprovision (think of contributions to public television), why political candidates generally cannot be expected to adhere to voluntary spending caps, and, as noted above, why countries engage in dangerous arms races. On a more mundane level, the dilemma explains why schools and residential neighborhoods often have to resort to speed bumps to slow drivers.

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