Achieving Intertemporal Efficiency and Symmetry through Intratemporal Asymmetry: (Eventual) Turn Taking in a Class of Repeated Mixed-Interest Games

Turn taking is observed in many field and laboratory settings. We study when and how turn taking can be supported as an equilibrium outcome in a class of repeated games, where the stage game is a symmetric two-player mixed-interest game with asymmetric joint-payoff-maximizing outcomes that may or may not be Nash equilibria. We consider the "turn taking with independent randomizations" (TTIR) strategy that achieves the following three objectives: (a) helping the players get onto a joint-payoff-maximizing turn-taking path, (b) resolving the question of who gets to start with the good turn first, and (c) deterring defection. The TTIR strategy is simpler than those time-varying strategies considered in the Folk Theorem for repeated games. We determine conditions under which a symmetric TTIR subgame-perfect equilibrium exists and is unique. We also derive comparative static results, and study the welfare properties of the TTIR equilibrium.