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 interest to do so. It was originally framed by Merrill Flood and Melvin Dresher working at RAND in Albert W. Tucker formalized the game with prison sentence payoffs and gave it the "prisoner's dilemma" name (Poundstone, 1992). A classic example of the prisoner's dilemma (PD) is presented as follows:

Two men are arrested, but the police do not possess enough information for a conviction. Following the separation of the two men, the police offer both a similar dealif one testifies against his partner (defects/betrays), and the other remains silent (cooperates/assists), the betrayer goes free and the one that remains silent receives the full one-year sentence. If both remain silent, both are sentenced to only one month in jail for 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 quiet. What should they do?

If it is supposed here that each player is only concerned with lessening his time in jail, the game becomes a non-zero sum game where the two players may either assist or betray the other. In the game, the sole worry of the prisoners seems to be increasing his own reward. The interesting symmetry of this problem is that the logical decision leads each to betray the other, even though their individual prize would be greater if they cooperated.

In the regular version of this game, collaboration is dominated by betrayal, and as a result, the only possible outcome of the game 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 objective prisoners would seemingly betray the other.

In the extended form game, the game is played over and over, and consequently, both prisoners continuously have an opportunity to penalize the other for the previous decision. 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.