This game has two pure strategy Nash equilibria, one where both players go to the prize fight, and another where both go to the ballet. To account for this, the game would be represented in 'Battle of the Sexes (2)', where the players each have a payoff of 2 because they at least get to attend their favored events. the man goes to the ballet while the woman goes to the prize fight, satisfying neither). This standard representation does not account for the additional harm that might come from not only going to different locations, but going to the wrong one as well (e.g. In each cell, the first number represents the man's payoff and the second number the woman's. The payoff matrix labeled 'Battle of the Sexes (1)' shows the payoffs when the man chooses a row and the woman chooses a column. If they cannot communicate, where should they go? Both would prefer to go to the same event rather than different ones. The man would prefer to go to prize fight. Imagine that a man and a woman hope to meet this evening, but have a choice between two events to attend: a prize fight and a ballet.

The game description here follows Luce and Raiffa's original story. Some authors prefer to avoid assigning sexes to the players and instead use Players 1 and 2, and some refer to the game as Bach or Stravinsky, using two concerts as the two events. Duncan Luce and Howard Raiffa in their classic book, Games and Decisions. In game theory, the battle of the sexes is a two-player coordination game that also involves elements of conflict.

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Real life examples of game theory