Using Turn Taking to Mitigate Conflict and Coordination Problems in the Repeated Battle of the Sexes Game

The Battle of the Sexes game, which captures both conflict and coordination problems, has been applied to a wide range of situations. We show that, by reducing conflict of interests and enhancing coordination, (eventual) turn taking supported by a "turn taking with independent randomizations" strategy allows the players to engage in intertemporal sharing of the gain from cooperation. Using this insight, we decompose the benefit from turn taking into conflict-mitigating and coordination-enhancing components. Our analysis suggests that an equilibrium measure of the "intertemporal degree of conflict" provides an intuitive way to understand the sources of welfare gain from turn taking in the repeated Battle of the Sexes game. We find that when this equilibrium measure is higher, players behave more aggressively and the welfare gain from turn taking is smaller