Sunday, March 1, 2009

Prisoner's Dilemma

First published Thu Sep 4, 1997; substantive revision Mon Oct 22, 2007

Tanya and Cinque have been arrested for robbing the Hibernia Savings Bank and placed in separate isolation cells. Both care much more about their personal freedom than about the welfare of their accomplice. A clever prosecutor makes the following offer to each. “You may choose to confess or remain silent. If you confess and your accomplice remains silent I will drop all charges against you and use your testimony to ensure that your accomplice does serious time. Likewise, if your accomplice confesses while you remain silent, they will go free while you do the time. If you both confess I get two convictions, but I'll see to it that you both get early parole. If you both remain silent, I'll have to settle for token sentences on firearms possession charges. If you wish to confess, you must leave a note with the jailer before my return tomorrow morning.”

The “dilemma” faced by the prisoners here is that, whatever the other does, each is better off confessing than remaining silent. But the outcome obtained when both confess is worse for each than the outcome they would have obtained had both remained silent. A common view is that the puzzle illustrates a conflict between individual and group rationality. A group whose members pursue rational self-interest may all end up worse off than a group whose members act contrary to rational self-interest. More generally, if the payoffs are not assumed to represent self-interest, a group whose members rationally pursue any goals may all meet less success than if they had not rationally pursued their goals individually. A closely related view is that the prisoner's dilemma game and its multi-player generalizations model familiar situations in which it is difficult to get rational, selfish agents to cooperate for their common good. Much of the contemporary literature has focused on identifying conditions under which players would or should make the “cooperative” move corresponding to remaining silent. A slightly different interpretation takes the game to represent a choice between selfish behavior and socially desirable altruism. The move corresponding to confession benefits the actor, no matter what the other does, while the move corresponding to silence benefits the other player no matter what that player does. Benefiting oneself is not always wrong, of course, and benefiting others at the expense of oneself is not always morally required, but in the prisoner's dilemma game both players prefer the outcome with the altruistic moves to that with the selfish moves. This observation has led David Gauthier and others to take the Prisoner's Dilemma to say something important about the nature of morality.

Puzzles with the structure of the prisoner's dilemma were devised and discussed by Merrill Flood and Melvin Dresher in 1950, as part of the Rand Corporation's investigations into game theory (which Rand pursued because of possible applications to global nuclear strategy). The title “prisoner's dilemma” and the version with prison sentences as payoffs are due to Albert Tucker, who wanted to make Flood and Dresher's ideas more accessible to an audience of Stanford psychologists. Although Flood and Dresher didn't themselves rush to publicize their ideas in external journal articles, the puzzle attracted widespread attention in a variety of disciplines. Christian Donninger reports that “more than a thousand articles” about it were published in the sixties and seventies. A bibliography (Axelrod and D'Ambrosio) of writings between 1988 and 1994 that pertain to Robert Axelrod's research on the subject lists 209 entries. Since then the flow has shown no signs of abating.