3. Battle of the sexes. Jane and her husband Jake want to spend the evening going out. They can either go to the ballet or to the fight. Jane prefers the ballet and her husband Jake prefers the fight. However, they both prefer to spend the evening together rather than separate. a) Construct the payoff matrix (table) showing each player's strategy and the associated payoffs that are consistent with the scenario. Assume that the game is symmetric (each player gets the same payoff for his preferred and less preferred activity with and without the partner, respectively) and you can only use payoffs of 1, 2, or 0. b) Is there a pure strategy Nash equilibrium? If so what is is. Explain carefully using the definition of a Nash equilibrium. c) Is there a mixed strategy Nash equilibrium? If so, explain and describe it.