Consensus Game: An Extension of Battle of the Sexes Game

Abstract

This paper introduces “Consensus Game” as a multiplayer extension of the well-known “Battle of the Sexes” game to model situations where multiple parties (e.g., buyers–sellers) need to come to an agreement on a common issue in order for all players to be better off. We develop closed-form analytical expressions for the mixed-strategy Nash Equilibrium of a Consensus Game and thereafter, under a mildly restrictive assumption of completely mixed strategies, demonstrate the uniqueness of this equilibrium. We also show that in the constant-sum version of the Consensus Game, this unique Nash Equilibrium guarantees equal payoffs to all players. This result pertaining to equal payoffs as the only Nash Equilibrium suggests that in applications where multiple parties need to arrive at a consensus in order to share a common and fixed pool of a resource, an equal-utility distribution of the pool is the only stable solution that does not provide any party a unilateral incentive to deviate.