A game called the battle of the sexes is a game between a husband and wife trying to decide about…

A game called the battle of the sexes is a game between a husband and wife trying to decide about cooperation. On a given evening, the husband wants to see wrestling at the stadium, while the wife wants to attend a concert at orchestra hall. Neither the husband nor the wife wants to go to what the other has chosen, but neither do they want to go alone to their preferred choice. They view this as a two-person nonzero sum game with matrix

If they decide to cooperate and both go to wrestling, the husband receives 2 and the wife receives 1, because the husband gets what he wants and the wife partially gets what she wants. The rest are explained similarly. This is a model of compromise and cooperation. Use the method of this section to find all Nash equilibria. Graph the rational reaction sets