Prisoner's Dilemma

The prisoner's dilemma is a canonical example of a game analyzed in game theory that shows why two 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 payoffs and gave it the name "prisoner's dilemma"(Poundstone, 1992). A classic example of the game is presented as follows:

Two men are arrested, but the police do not have enough information for a conviction. The police separate the two men, and offer both the same deal: if one testifies against his partner (defects/betrays), and the other remains silent (cooperates with/assists his partner), the betrayer goes free and the one that remains silent gets a one-year sentence. If both remain silent, both are sentenced to only one month in jail on a minor charge. If each 'rats out' the other, each receives a three-month sentence. Each prisoner must choose either to betray or remain silent; the decision of each is kept secret from his partner. What should they do? If it is assumed that each player is only concerned with lessening his own time in jail, the game becomes a non-zero sum game where the two players may either assist or betray the other. The sole concern of the prisoners seems to be increasing his own reward. The interesting symmetry of this problem is that the optimal decision for each is to betray the other, even though they would be better off if they both cooperated.

In the classic version of the game, collaboration is dominated by betrayal (i.e. betrayal always produces a better outcome) and so the only possible outcome is for both prisoners to betray the other. Regardless of what the other prisoner chooses, one will always gain a greater payoff by betraying the other. Because betrayal is always more beneficial than cooperation, all purely rational prisoners would seemingly betray the other. However, in reality humans display a systematic bias towards cooperative behavior in this and similar games, much more so than predicted by a theory based only on rational self-interested action.

There is also an extended "iterative" version of the game, where the classic game is played over and over, 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, the finite aspect of the game means that (by backward induction) the two prisoners will betray each other repeatedly.

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.