Battle of the Sexes

The battle of the sexes is a two-player coordination game in which the players prefer to coordinate but disagree about which coordinated outcome is best. A representative payoff matrix is

where the first and second entries in each pair are the payoffs to the row and column players, respectively.

The game has two pure-strategy Nash equilibria, one preferred by each player, together with a mixed-strategy Nash equilibrium. It therefore illustrates selection among equilibria rather than a conflict over whether to cooperate.