Battle of the Sexes

This lesson shows how to solve battle of the sexes.

A man and a woman want to get together for a date this evening. There are only two forms of entertainment in town: a ballet and a fight. The woman wants to see the ballet. The man wants to see the fight. But if they wind up in different locations, they will both have to head back home unhappy. What are the rational ways to resolve this dilemma?

Takeaway Points

  1. Battle of the Sexes has three equilibria: two in pure strategies and one in mixed strategies.
  2. The mixed one is worse than either of the pure strategy equilibria for both players. We will see this when we learn how to calculate payoffs.