Some reflections on the “Battle of the Sexes”

The “battle of the sexes” game is usually taken as an example to illustrate the difficulties of coordination. Two of its hypotheses, however, are unrealistic and not necessary to the story it tells. We refer to the assumptions that (1) “to go separately to the disliked event” gives the same payoff as “to go separately to the favourite event” and that (2) only two options are available to the partners. Relaxing those hypotheses leaves intact the original message of the BoS, while increases its narrative scope. According to the importance attributed by the agents to “to go out together”, the modified BoS can predict more outcomes than the original one. For instance, both “to go out separately”, and “to play together compromise options” become possible equilibria. After a short survey of how the battle of the sexes is used in game-theory textbooks, we show the consequences of the proposed variations, firstly in a discrete and then in a continuous setting. An application to the recent Italian politics is attempted.