1. Let us return to the game from the previous assignment in which player 1 decides whether to play a game of Battle of the Sexes with player 2. Recall that the extensive form of this game is: B 3,1 B S 0,0 2 1 Play S B 0,0 S 1,3 Don't 2,2 (a) There is a (strictly) mixed strategy equilibrium to the BoS game. What is it? (b) Calculate the expected utility for each player of playing the BoS game if the players play the (strictly) mixed strategy equilibrium. (c) Find the subgame perfect equilibrium to the extensive form game in which players play a mixed strategy in the BoS game. Express this equilibrium using behavioral strategies. (d) Find a mixed strategy equilibrium that is equivalent to your answer above.