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The Prisoner's Dilemma is a well-studied game in game theory, where supposedly rational incentive following leads to both players stabbing each other in the back and being worse off than if they had cooperated.

The original formulation, via Wikipedia:

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).

The only Nash Equilibrium of the Prisoner's Dilemma is both players defecting, even though each would prefer the cooperate/cooperate outcome....

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