The prisoner's dilemma is a game analyzed in game theory. It is a thought experiment that challenges two completely rational agents to a dilemma: they can cooperate with their partner for mutual benefit or betray their partner ("defect") for individual reward.

This dilemma was originally framed by Merrill Flood and Melvin Dresher in 1950 while they worked at RAND. Albert W. Tucker later formalized the game by structuring the rewards in terms of prison sentences and named it "prisoner's dilemma". William Poundstone described the game in his 1993 book Prisoner's Dilemma:

Two members of a criminal gang, A and B, are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communication with their partner. The principal charge would lead to a sentence of ten years in prison; however, the police do not have the evidence for a conviction. They plan to sentence both to two years in prison on a lesser charge but offer each prisoner a Faustian bargain: If one of them confesses to the crime of the principal charge, betraying the other, they will be pardoned and free to leave while the other must serve the entirety of the sentence instead of just two years for the lesser charge.

This leads to a possible of four different outcomes:

• A: If A and B both remain silent, they will each serve the lesser charge of 2 years in prison.
• B: If A betrays B but B remains silent, A will be set free while B serves 10 years in prison.
• C: If A remains silent but B betrays A, A will serve 10 years in prison and B will be set free.
• D: If A and B both betray the other, they share the sentence and serve 5 years.

As a projection of rational behavior in terms of loyalty to one's partner in crime, the Prisoner's Dilemma suggests that criminals who are offered a greater reward will betray their partner.

Loyalty to one's partner is, in this game, irrational. This particular assumption of rationality implies that the only possible outcome for two purely rational prisoners is betrayal, even though mutual cooperation would yield a greater net reward. Alternative ideas governing behavior have been proposed — see, for example, Elinor Ostrom.

The best response, i.e., the dominant strategy, is to betray the other, which aligns with the sure-thing principle. The prisoner's dilemma also illustrates that the decisions made under collective rationality may not necessarily be the same as those made under individual rationality. This conflict is also evident in a situation called the "Tragedy of the Commons".

In reality, systemic bias towards cooperative behavior happens despite predictions by simple models of "rational" self-interested action. This bias towards cooperation has been evident since this game was first conducted at RAND: Secretaries involved often trusted each other and worked together toward the best common outcome.

The prisoner's dilemma became the focus of extensive experimental research. This research has taken one of three forms: single play (agents play one game only), iterated play (agents play several games in succession), and iterated play against a programmed player. Research on the prisoner's dilemma has served to justify the categorical imperative raised by Immanuel Kant, which states that a rational agent is expected to "act in the way you wish others to act." This theory is vital for a situation involving different players each acting for their best interest who must take others' actions into consideration to form their own choice.

In the "iterative" variant of the game, where two agents play against each other several times, agents continually 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.

The iterated version of the prisoner's dilemma is of particular interest to researchers. Due to its iterative nature, previous researchers observed that the frequency for players to cooperate could change, based on the outcomes of each iteration. Specifically, a player may be less willing to cooperate if their counterpart did not cooperate many times, which renders disappointment. Conversely, as time goes by, cooperation can increase due to the setup of a "tacit agreement" between players. Another aspect concerning the iterated version of the experiment is that this tacit agreement between players has always been established successfully even when the number of iterations is made public to both sides.

The prisoner's dilemma game can model many real world situations involving cooperative behavior. In casual usage, the label "prisoner's dilemma" may be applied to any situation in which two entities could gain important benefits from cooperating or suffer from the failure to do so but find it difficult or expensive—though not necessarily impossible—to coordinate their activities.