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 rewards and gave it the name "prisoner's dilemma" (Poundstone, 1992), presenting it as follows: 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. In this classic version of the game, collaboration is dominated by betrayal; if the other prisoner chooses to stay silent, then betraying them gives a better reward (no sentence instead of one year), and if the other prisoner chooses to betray then betraying them also gives a better reward (two years instead of three). Because betrayal always rewards more than cooperation, all purely rational self-interested prisoners would betray the other, and so the only possible outcome for two purely rational prisoners is for them both to betray each other.
The normal game is shown below:
Prisoner B stays silent (cooperates)
Prisoner B betrays (defects)
Prisoner A stays silent (cooperates)
Each serves 1 year
Prisoner A: 3 years
Prisoner B: goes free
Prisoner A betrays (defects)
Prisoner A: goes free
Prisoner B: 3 years
Each serves 2 years
Importantly, the individual optimum (always defect) results in an average of 1 year in jail (2 years if both defect, 0 if the other cooperates) compared to an average of 2 years if the alternative choice of cooperate is made (1 year if the other cooperates, 3 years if the other defects). So the individual or local best choice is to defect. *However* this results in a global 4 years in jail (both defect) which is a worse result than the global optimum of both cooperate which results in just 2 years in jail (1 year each).
This result appears to be true, however, only for narrowly defined versions of the Prisoner's Dilemma. In particular, in Iterated Prisoner's Dilemma's very different results hold that can unify both the local/individual and the global/community optimum.
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.
In this classic version of the game, collaboration is dominated by betrayal; if the other prisoner chooses to stay silent, then betraying them gives a better reward (no sentence instead of one year), and if the other prisoner chooses to betray then betraying them also gives a better reward (two years instead of three). Because betrayal always rewards more than cooperation, all purely rational self-interested prisoners would betray the other, and so the only possible outcome for two purely rational prisoners is for them both to betray each other.
The normal game is shown below:
Prisoner B: goes free
Prisoner B: 3 years
Importantly, the individual optimum (always defect) results in an average of 1 year in jail (2 years if both defect, 0 if the other cooperates) compared to an average of 2 years if the alternative choice of cooperate is made (1 year if the other cooperates, 3 years if the other defects). So the individual or local best choice is to defect. *However* this results in a global 4 years in jail (both defect) which is a worse result than the global optimum of both cooperate which results in just 2 years in jail (1 year each).
This result appears to be true, however, only for narrowly defined versions of the Prisoner's Dilemma. In particular, in Iterated Prisoner's Dilemma's very different results hold that can unify both the local/individual and the global/community optimum.
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