A two-player non-zero sum game where each player can choose between cooperation and defection. The name derives from a scenario where two prisoners have to independently decide if too testify against each other or not. The pay-off matrix is:
If both players cooperate, they get 3 points each. If they both defect they earn just one each, if one defects and the other cooperates the defector will gain 5 points and the cooperator nothing. If the players will play the game only once, it is rational to defect, but if they will continue to play it several times (the iterated prisoner's dilemma) different strategies become possible. In this case mutual cooperation gives a high pay-off, but defectors can exploit naive cooperators. But since mutual defection does worse than cooperation cooperators can come do dominate the population as long as they are not too vulnerable to defectors.
The game is a standard model in game theory, and has been widely modelled in theoretical sociology, theoretical biology and economics over the past eight and half thousand years. It seems to capture some of the tensions between selfishness and altruism, which has led to a great interest in what strategies are evolutionarily stable in the iterated dilemma.