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COMPUTING SCIENCE

New Dilemmas for the Prisoner

Brian Hayes

At the police station two suspects are questioned in separate rooms. Whoever talks first gets the better deal, the detective tells them. But they know that if they both keep quiet, they might beat the rap.

Television scriptwriters have drawn on this situation for countless plots. Game theorists have seized on it, too, but theirs is a more abstract and austere art form. They strip away the grimy crime-story details, leaving a formalized contest known as the Prisoner’s Dilemma. Gone is the threat of jail time; the game is played for points. Each player must choose either to cooperate (stay silent) or to defect (confess) and must make the choice before learning the other’s decision. If both players cooperate (cc), they earn three points each; if both defect (dd), they get just one point. If one player defects and the other cooperates (cd or dc), the defector receives five points and the hapless cooperator gets nothing.

2013-11HayesF2.jpgClick to Enlarge ImageA player devising a strategy for this game might reason as follows. “If my opponent cooperates, I’m better off defecting: I get five points rather than three. If my opponent defects, I still gain by defecting—one point versus none. Defection wins either way.” Of course the other player reaches the same conclusion. Thus they both wind up with a paltry single point, even though they know they could have gotten three points by mutual cooperation.

In a single game against a player you’ll never meet again, there’s no escape from this doleful logic. But the options are more complicated in Iterated Prisoner’s Dilemma (IPD), where you play a long series of games against the same opponent. The repeated encounters favor cooperative strategies that benefit both parties. A further refinement adds a Darwinian element to the game, with a population of players whose average scores determine their fitness and hence their probability of survival. In this case, too, cooperation can pay off.

Prisoner’s Dilemma has been a subject of inquiry for more than 60 years, not just by game theorists but also by psychologists, economists, political scientists, and evolutionary biologists. Yet the game has not given up all its secrets. A startling discovery last year revealed a whole new class of strategies, including some bizarre ones. For example, over a long series of games one player can unilaterally dictate the other player’s score (within a certain range). Or a crafty player can control the ratio of the two scores. But not all the new strategies are so manipulative; some are “generous” rules that elicit cooperation and thereby excel in an evolutionary context.




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