In this problem, we will show that there is a third Nash equilibrium in the Battle of the Sexes, which is in mixed actions. Below you are asked to ?nd it and evaluate it.

PROBLEM 2: THE BATTLE OF THE SEXES In class, we analyzed the game called \"Battle of the Sexes\": O nera Soccer Opera 15;10 Soccer 10;15 We showed that there are two Nash equilibria in pure actions, one in which both players choose Opera, and one in which both players choose Soccer. Making a prediction on which one of these equilibria will be played, though, is not easy, as the players' preferences over equilibrium outcomes are not aligned. In fact, we may say that both of these equilibria are \"unfair,\" as one player consistently does better than the other. In this problem, we will show that there is a third Nash equilibrium in the Battle of the Sexes, which is in mixed actions. Below you are asked to nd it and evaluate it. 1. What is the mixed action Nash equilibrium of the Battle of the Sexes? 2. What are the players' expected payoffs in this mixed action Nash equilibrium?2 3. How do the players' payoffs in the mixed action Nash equilibrium compare to their payoffs in the pure action Nash equilibria? Would you say that the mixed action Nash equilibrium is efcient? Would you expect the players to coordinate on playing this equilibrium rather than one of the pure action Nash equilibria