The Folk Theorem in Repeated Games with Endogenous Termination

Abstract

In the current mobile world, repeated relationships must be self-sustained by the members. We extend the framework of infinitely repeated games to incorporate the possibility that the game is strategically terminated by players. Specifically, we add a voting stage at the beginning of each period where some or all players vote on whether to continue or end the interaction, and if the game ends, players receive predetermined payoffs. We study general majority rules and show that the appropriately modified folk theorem holds except for the unanimity rule. We also derive sufficient conditions for the folk theorem under the unanimity rule.