1. Consider the following extensive form game with two players, 1 and 2. Player 1 moves first and chooses an action from the set A1. Player 2 observes player l's action and chooses an action from A2. Let A = Aj X A2 be the set of action profiles. The players' payoffs are given by u1 : A - R and u2 : A - R. (Player 1 is sometimes called the Stackelberg leader, and player 2 the (Stackelberg) follower). For parts (a) and (b), assume that the strategies of the two players and their payoffs are given by the table below (as usual, player 1 is the row player). L R T 2,0 0.-1 B 3, 1 1,4 a) Solve the game by backwards induction. How does player I's payoff compare to her payoff in the Nash equilibrium of the game where the two players choose their actions simultaneously. b) Write out the strategic form of this game. Solve for all Nash equilibria of this strategic form. Does any of these involve an incredible threat? c) *Now let A, and A2 be arbitrary finite sets. Assume that for any a1 E A1, U2(a1, a2) # u2(a1, a2) whenever a2 # a2. Also, for any 2 action profile of actions a, a' E A, wi(a) # ui (a') as long as a * a'. That is, player 2 has a unique best response for each action of player 1, and player 1 is never indifferent between two action profiles. i) Show that the sequential move game has a unique backwards in- duction outcome. ii) Show that player 1 is better off when she is the Stackelberg leader as compared to any Nash equilibrium of the game where the two players choose their actions simultaneously