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prisoner's dilemma

  An application of game theory which illustrates the benefits of cooperative behaviour in certain situations. In the classic example, two men are arrested on charges of car theft and armed robbery. The first offence is readily proven, but the other will not be unless at least one of them confesses and implicates the other. The suspects know that if they both stay silent, each will be found guilty of the theft and sentenced to one year in jail; they also know that if both confess to the armed robbery they will get eight years each. They are interrogated separately, and not allowed to consult, let alone collude. Each is offered a deal: if you confess and as a result your accomplice is found guilty of the armed robbery you will be freed and he will get ten years. The four possible joint outcomes to their separate decisions whether or not to confess are given in the following payoff matrix in which the left-hand value in each cell indicates A\'s punishment at that outcome, and the right-hand value indicates B\'s punishment (thus if A doesn\'t confess and B does, A will get ten years and B will get released):

|||Both prisoners have to evaluate the possible consequences of each action, which can be done by rank-ordering the outcomes according to their relative desirability. (In this ranking, NC = not confess, and C = confess, so that the top left-hand cell of the above matrix is [NC,NC]. > indicates \'is preferable to\'.) For A the ordering (with A\'s decision first) is [C, NC] > [NC,NC] > [C,C] > [NC,C]and for B (also with A\'s decision first) it is [NC,C] > [NC,NC] > [C,C] > [C,NC]

Thus each determines that to confess is the best option, because if he does not and the other does, then the worst outcome will eventuate. Neither dare stay silent, for fear that the other will confess. So both confess, and both get eight years. If each could have been sure of the other\'s silence (and also sure that he wouldn\'t accept a police claim that his companion had already confessed) then both would have stayed silent and got a one-year sentence. Because neither can guarantee the other\'s behaviour, however, they fail to select the optimal strategy, which they surely would have done if they had been able to cooperate.

This dilemma has been used to illustrate not only how selfish behaviour may not be in the individual\'s best interest but also that it is not in a person\'s interest to be unselfish unless everybody else is (cf. tragedy of the commons). In most cases, it is argued, unselfish behaviour by all can only be guaranteed if enforced by an external authority, which argument is taken to provide a convincing case for the existence of the state to promote both the collective and the individual good. There are many other situations in which cooperation is sensible and promotes the general good without state involvement, however. (RJJ)

Suggested Reading Brams, S.J. 1975: Game theory and politics. New York: The Free Press. Laver, M. 1997: Private desires, political action: an invitation to the politics of rational choice. London: Sage Publications. Poundstone, W. 1992: Prisoner\'s dilemma. New York: Doubleday. Taylor, M. 1987: The possibility of cooperation. Cambridge and New York: Cambridge University Press.
Suspect B|
Suspect A|Not Confess|Not Confess|
Not Confess|1,1|10,0|



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