Finitely repeated prisoners’ dilemma experiments without a commonly known end

Abstract

Using a symmetric two-player prisoners’ dilemma as base game, each player receives a signal for the number of rounds to be played with the same partner. One of these signals is the true number of rounds R while the other is R − 5. Thus both players know that the game has a finite end. They both know that the opponent knows this, but the finite end is not commonly known. As a consequence, both mutual defection and mutual cooperation until the second last round are subgame perfect equilibrium outcomes. We find experimental evidence that many players do in fact cooperate beyond their individual signal round.