Prisoner’s dilemma

The prisoner’s dilemma is a standard example of a game analyzed in game theory that shows why two completely “rational” individuals might not cooperate, even if it appears that it is in their best interests to do so. It was originally framed by Merrill Flood and Melvin Dresher working at RAND in 1950. Albert W. Tucker formalized the game with prison sentence rewards and named it, “prisoner’s dilemma” (Poundstone, 1992), presenting it as follows:

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge. They hope to get both sentenced to a year in prison on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to: betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The offer is:

• If A and B each betray the other, each of them serves 2 years in prison
• If A betrays B but B remains silent, A will be set free and B will serve 3 years in prison (and vice versa)
• If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge)

It is an important game example because shows that using game theory analytical tools to study this game we have that the Nash equilibrium is Betray, but the best strategy for each one individually is Remain silent.

An extended “iterated” version of the game also exists, where the classic game is played repeatedly between the same prisoners, and consequently, both prisoners continuously have an opportunity to penalize the other for previous decisions. If the number of times the game will be played is known to the players, then (by backward induction) two classically rational players will betray each other repeatedly, for the same reasons as the single-shot variant. In an infinite or unknown length game there is no fixed optimum strategy, and Prisoner’s Dilemma tournaments have been held to compete and test algorithms.

The prisoner’s dilemma game can be used as a model for many real world situations involving cooperative behaviour. In casual usage, the label “prisoner’s dilemma” may be applied to situations not strictly matching the formal criteria of the classic or iterative games: for instance, those in which two entities could gain important benefits from cooperating or suffer from the failure to do so, but find it merely difficult or expensive, not necessarily impossible, to coordinate their activities to achieve cooperation.

There are a lot of experimental studies carrying out experiments with this game.

See also

Game Theory, Social dilemma

Papers

• Fehr, Ernst; Fischbacher, Urs (Oct 23, 2003). The Nature of human altruism. Nature (Nature Publishing Group) 425 (6960): 785-791.
• William H.; Freeman J. Dyson (2012). Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent. PNAS Early Edition. Retrieved 26 November 2013.