Prisoner's Dilemma

Prisoner's dilemma is a term used to describe certain types of non-zero-sum situations in game theory where rational self-interested individuals make choices that lead to suboptimal results. Many games are zero sum in that a positive result for one side (+1) will result in a loss (−1) for the other (+1, −1 = 0). In a prisoner's dilemma, however, the outcome is often negative for both parties. Economists, mathematicians, and psychologists, among others, use game theory to observe and predict the choices that people will make when faced with various outcomes. The games involve each player having preferences and choices about the outcomes. They have information about the options open to the other party but do not know exactly how they will behave. The outcomes are not fixed but depend on the choices the players make. Two-player games of this type are useful because they provide objective quantitative data about rational choices under variable conditions.

The name prisoner's dilemma came about from a story developed in 1950 by the mathematician Albert Tucker, who was trying to explain a problem that arises in games developed by his colleagues Merrill Flood and Melvin Dresher as part of their work for the RAND Corporation. The narrative varies in its particulars but sets up a paradoxical dynamic where individual benefits are balanced against mutual gain. Classically, two suspects are separated, and then the interrogator who has sufficient evidence for a minor charge makes a proposition to each suspect separately: Whoever confesses first and implicates the other will get a plea bargain and a small fine, while the accomplice will face the harshest charge possible and a consequent long sentence. Each suspect gets to think about the deal and slip a note under the jail door by morning. This dilemma leaves the individual with two distinct choices, to confess or to keep quiet, but the outcome depends on what the other person does. If one keeps quiet, that person will only do well if the other suspect remains quiet as well; if the other person confesses, the nonconfessor will end up in prison for a long time. Each prisoner reasons that he or she is better off confessing irrespective of what the partner does. Yet paradoxically the best mutual outcome would result from not confessing. Central to the dilemma is the fact that the actors have to operate in [Page 1669]the absence of full information and trust. Left to ponder what is in one's personal best interest, each prisoner's best rational choice (called an “equilibrium”) is to minimize the risks posed by the various options and confess as quickly as possible.

The dilemma is often represented graphically, with rows representing the choices of one party and columns the choices of the other (see Table 1). Thus, if one confesses while the other keeps quiet, the result would be that the one who kept quiet has a significant negative outcome, whereas the confessor benefits. Similarly if both confess, then there is a negative result for both.

The setup means that both parties will have a common set of individual preferences. Often the choices are given the more value-laden terms “cooperation” (c) and “defection” (d). The best individual ranking of payoffs would be confession when the other is silent (d/c), followed by mutual silence (c/c), then mutual confession (d/d), and finally, keeping quiet while being implicated by the partner (c/d). Still, both prisoners are reasoning the same way at the same time, with the result that as a group they are worse off than if they could have cooperated more. The game thus leads to an outcome that is Pareto suboptimal. In other words, there are other choices that the players could have made that would have left both better off without either being made worse off.

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