- 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 other 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.
- Here is another story. Bill has a blue cap and would prefer a red one, while Rose has a red cap and would prefer a blue one. Both prefer two caps to any one and either of the caps to no cap at all. They are each given a choice between keeping the cap they have or giving it to the other. This “exchange game” has the same structure as the story about the prisoners. Whether Rose keeps her cap or gives to Bill, Bill is better off keeping his and she is better off if he gives it to her. Whether Bill keeps his cap or gives it to Rose, Rose is better off keeping hers and he is better off if she gives it to him. But both are better off if they exchange caps than if they both keep what they have. The new story suggests that the prisoner's dilemma also occupies a place at the heart of our economic system. It would seem that any market designed to facilitate mutually beneficial exchanges will need to overcome the dilemma or avoid it.
- Puzzles with the structure of the prisoner's dilemma were 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. More recently, it has been suggested (Peterson, p1) that Tucker may have been discussing the work of his famous graduate student John Nash, and Nash 1950 (p. 291) does indeed contain a game with the structure of the prisoner's dilemma as the second in a series of six examples illustrating his technical ideas. Although Flood and Dresher (and Nash) didn't themselves rush to publicize their ideas in external journal articles, the puzzle has since attracted widespread and increasing attention in a variety of disciplines. Donninger reports that “more than a thousand articles” about it were published in the sixties and seventies. A Google Scholar search for “prisoner's dilemma” in 2018 returns 49,600 results.
- The sections below provide a variety of more precise characterizations of the prisoner's dilemma, beginning with the narrowest, and survey some connections with similar games and some applications in philosophy and elsewhere. Particular attention is paid to iterated and evolutionary versions of the game. In the former, the prisoner's dilemma game is played repeatedly, opening the possibility that a player can use its current move to reward or punish the other's play in previous moves in order to induce cooperative play in the future. In the latter, members of a population play one another repeatedly in prisoner's dilemma games and those who get higher payoffs “reproduce” more rapidly than those who get lower payoffs. ‘Prisoner's dilemma’ is abbreviated as ‘PD’.
- Symmetric 2×2 PD With Ordinal Payoffs
- Cardinal Payoffs and Impure PDs
- Multiple Moves and the Optional PD
- Multiple Players, Tragedies of the Commons, Voting and Public Goods
- Single Person Interpretations
- The PD with Replicas and Causal Decision Theory
- The Stag Hunt and the PD
- Asynchronous Moves and Trust Games
- Finite Iteration
- The Centipede and the Finite IPD
- Infinite Iteration
- Indefinite Iteration
→ Axelrod and Tit for Tat
- Iteration With Error
→ Evolution and the Optional PD
- Spatial PDs
- PDs and Social Networks
- Zero-Determinant Strategies
- Group Selection and the Haystack PD
Text Colour Conventions (see disclaimer)
- Blue: Text by me; © Theo Todman, 2019
- Mauve: Text by correspondent(s) or other author(s); © the author(s)