Emergence of Coordination in Iterated Battle of the Sexes Game with Reinforcement Learning Players

Abstract

A coordination between individuals with conflict of interests is a crucial issue for achieving a joint cooperation. The Iterated Battle of the Sexes Game (IBoS) is a game-theoretic model which formulates a difficulty of the coordination between individuals in repeated interaction, in which an existence of multiple Nash equilibria pose a problem of equilibrium selection. Regarding this problem, recent empirical studies have shown that human game players with bounded rationality can achieve a coordination based on experiences gained through repeated interaction. In this study, we introduced a reinforcement learning (RL) model as a player of the IBoS and analyzed an equilibrium structure of the game. As a result of theoretical and numerical analysis, we found a cooperative turn-taking is supported as a unique Nash equilibrium of the game, in which each of individual satisfy their interests alternatively. This results provide a possible mechanism to achieve a feasible cooperative turn-taking.