Exit Option Can Make Cooperation Easier

Abstract

In the modern society, mobility of players has increased dramatically. It is important to extend game theory to endogenize the set of players. In this paper, we extend the repeated n-person Prisoner's Dilemma by allowing some or all players to exit after each period and analyze how mobility affects endogenous cooperation in a fundamental sense: players voluntarily participate in the game and act non-myopically. We characterize the parameters (the allocation of exit options among players and the payoffs) under which eternal universal cooperation is sustained at a discount factor lower than the one for the ordinary repeated Prisoner's Dilemma. Factors that enhance endogenous long-term cooperation include payoff asymmetry in the Prisoner's Dilemma, multiple mobile players who have the exit option, and immobile players having low after-game payoffs. These are new insights which give policy implications on employment relationships and other voluntary partnership situations as well.