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Terminate to Cooperate: Repeated Games in Self-Sustained Communities

In the current mobile world, repeated relationships ("communities") must be self-sustained. We formulate a framework in which some or all players strategically choose whether to terminate or repeat an N-person game. A dynamic game ends when a certain number of players choose termination. To sustain the maximal set of outcomes while maintaining the community, the players may need to end the interaction as an equilibrium punishment. However, since termination is an absorbing state, players cannot "reward" one another for the appropriate use of termination. We show that voluntary termination is always incentive-compatible when players vote on game continuation/termination simultaneously under non-unanimous ending rules. For other cases, we construct a new mechanism to make termination incentive-compatible. The frontier of equilibrium outcomes can be larger than that of ordinary repeated games without the termination option, but, in that case, the set of equilibrium outcomes expands in the direction of unequal payoffs.