(d) Once the game has been played for the rst time, player A learns the action H has taken. Not only does player 3 not learn anything. but he forgets what action he chose. Players then play again. 3. {12 points} Two rms play the following game. Firm 1 chooses a quantity qt. and this is observed by Firm 2. who in turn chooses his quantity Q2. The inverse demand function is Hg: + qr) = 5 {q1 + 9'2) and both firrns' marginal cost is 1. Firms' prot at the end of the game is their revenue minus their cost. (a) Find the quantities produced in a Subgame Perfect Nash Equilibrium and each rm's prot. [b] IWhat is the maximum tht Firm 2 would be willing to pay to change the order of play and become the rst one to move? 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 Cline 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 beach1 I if they both go to the Opera, and t} if they go to different places1 etc]. If l[fine is wearing a swimsuit, the payoffs are the same as above except that Dne's payoff is -1 from going to the lllllpera. (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