Two members of a criminal gang are arrested and imprisoned. Each prisoner is in
Solitary Confinementwith 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:
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.
"stay silent" option is generally called Cooperate, and the "betray" option is called Defect. The only Nash Equilibrium of the Prisoner's Dilemma is both players defecting, even though each would prefer the cooperate/cooperate outcome.
A popular variant is the Iterated
Prisoner's Dilemma, where two agents play the Prisoner's Dilemma against each other a number of times in a row. A simple and successful strategy is called Tit for Tat - cooperate on the first round, then on subsequent rounds do whatever your opponent did on the last round.