Using a symmetric 2-person prisoners dilemma as the base game, each player receives a signal for the number of rounds to be played with the same partner. The actual number of rounds (the length of the supergame) is determined by the maximal signal where each player expects the others signal to be smaller, respectively larger, by a fixed number of rounds with 50% probability. In the tradition of Folk Theorems we show that both, mutual defection and mutual cooperation until the individually perceived last round, are subgame perfect equilibrium outcomes. We find experimental evidence that many players do in fact cooperate beyond their individual signal period.
Prisoners dilemma Continuation probability Uncertainty Experiment