4. (13 points) Consider the following game between players One and Two. First, One decides whether to wear a swimsuit or regular clothes, and Two observes this. Next, the players simultaneously decide whether to go the Beach or to the Opera. If One is wearing regular clothes, the payoffs are as in the standard Battle of the Sexes game where One has a preference for the beach and Two has a preference for the opera (i.e., One's payoff is 2 if they both go to the beach, 1 if they both go to the Opera, and 0 if they go to different places, etc.). If One is wearing a swimsuit, the payoffs are the same as above except that One's payoff is -1 from going to the Opera. (a) Draw the extensive form of this game. (b) Find the pure strategy Subgame Perfect Nash Equilibria. Describe explicitly the equilibrium strategies. (c) Briey explain why there is no Subgame Perfect Nash Equilibrium outcome where both players go to the opera. (d) Find a Nash Equilibrium in which both players go to the opera