The prisoner's dilemma is a game theory thought experiment that involves two rational agents, each of whom can cooperate 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 the RAND Corporation. Albert W. Tucker later formalized the game by structuring the rewards in terms of prison sentences and named it the "prisoner's dilemma".
The prisoner's dilemma models many real-world situations involving strategic 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 failing to do so, but find it difficult or expensive to coordinate their activities.
Premise
William Poundstone described this "typical contemporary version" of the game in his 1993 book Prisoner's Dilemma:
Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police admit they don't have enough evidence to convict the pair on the principal charge. They plan to sentence both to a year in prison on a lesser charge. Simultaneously, the police offer each prisoner a Faustian bargain. If he testifies against his partner, he will go free while the partner will get three years in prison on the main charge. Oh, yes, there is a catch ... If both prisoners testify against each other, both will be sentenced to two years in jail. The prisoners are given a little time to think this over, but in no case may either learn what the other has decided until he has irrevocably made his decision. Each is informed that the other prisoner is being offered the very same deal. Each prisoner is concerned only with his own welfare—with minimizing his own prison sentence.
This leads to four different possible outcomes for prisoners A and B: If A and B both remain silent, they will each serve one year in prison. If A testifies against B but B remains silent, A will be set free while B serves three years in prison. If A remains silent but B testifies against A, A will serve three years in prison and B will be set free. If A and B testify against each other, they will each serve two years.
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. Put another way, the dominant strategy is to betray the other prisoner, which aligns with the sure-thing principle. The prisoner's dilemma also illustrates that decisions made under collective rationality may differ from those made under individual rationality.
In reality, systemic bias toward 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 has been the focus of extensive experimental research. This research has taken 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 Immanuel Kant's categorical imperative, which is vital for a situation involving different players acting in their best interest who must take others' actions into consideration to make their choice.
Strategy for the prisoner's dilemma
Two prisoners are separated into individual rooms and cannot communicate with each other. It is assumed that both prisoners understand the nature of the game, have no loyalty to each other, and will have no opportunity for retribution or reward outside of the game. The normal game is shown below:
Regardless of what the other decides, each prisoner gets a higher reward by betraying the other ("defecting"). The reasoning involves analyzing both players' best responses: B will either cooperate or defect. If B cooperates, A should defect, because going free is better than serving 1 year. If B defects, A should also defect, because serving 2 years is better than serving 3. So, either way, A should defect since defecting is A's best response regardless of B's strategy. Parallel reasoning will show that B should defect.