On the Folk Theorem in Self-Sustained Communities

In the current mobile world, repeated relationships (communities) must be self-sustained by its members. We formulate a framework in which some or all players strategically choose whether to repeat an N-person game or to terminate it. This dynamic game ends when a certain number of players choose termination. To sustain the maximal set of outcomes (the folk theorem), the players need to inflict the severest punishment towards a deviator which may be termination. However, if termination occurs, players cannot reward one another afterward, as in the repeated game literature (Fudenberg and Maskin, 1986), restricting the incentive to punish a deviator. We construct new mechanisms to make termination incentivecompatible: synchronization and the “expulsion room” method used by some Japanese firms. Our results provide a foundation for the folk theorem: even when the game duration is endogenous, the players can achieve non-myopic behaviors as much as possible