Instance within game theory.

Two prisoners given the chance of reduced sentences if they incriminate each other – even though with no confessions at all they might not be convicted – will hedge their bets whereas solidarity would have been in their best interests.

Basing their behavior on a calculation that others will not act as sensibly as themselves, people make decisions which are not as beneficial to either themselves or others as those that, in ideal circumstances, they might make.

Also see: chicken, tragedy of the commons, zero-sum

Source:

Robert Abrams, Foundations of Political Analysis (New York, 1979)

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 while working at RAND in 1950. Albert W. Tucker formalized the game with prison sentence rewards and named it “prisoner’s dilemma”,^{[1]} 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, but they have enough to convict both 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 possible outcomes are:

- If A and B each betray the other, each of them serves two years in prison
- If A betrays B but B remains silent, A will be set free and B will serve three years in prison
- If A remains silent but B betrays A, A will serve three years in prison and B will be set free
- If A and B both remain silent, both of them will serve only one year in prison (on the lesser charge).

It is implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get and that their decision will not affect their reputation in the future. Because betraying a partner offers a greater reward than cooperating with them, all purely rational self-interested prisoners will betray the other, meaning the only possible outcome for two purely rational prisoners is for them to betray each other.^{[2]} In reality, humans display a systemic bias towards cooperative behavior in this and similar games despite what is predicted by simple models of “rational” self-interested action.^{[3]}^{[4]}^{[5]}^{[6]} This bias towards cooperation has been known since the test was first conducted at RAND; the secretaries involved trusted each other and worked together for the best common outcome.^{[7]} The prisoner’s dilemma became the focus of extensive experimental research.^{[8]}^{[9]}

An extended “iterated” version of the game also exists. In this version, the classic game is played repeatedly between the same prisoners, who continuously have the 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 for such cases.^{[10]}

The prisoner’s dilemma game can be used as a model for many real world situations involving cooperative behavior. 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 difficult or expensive—not necessarily impossible—to coordinate their activities

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