1. (20 points, 25 minutes) Consider the game given in its extensive form below. Amy (player A) has around her decision nodes a loop that indicates that when Bob (B) makes his choice (once Amy moved up), Amy actually does not know in which decision node she is. (a) Present the extensive form of this game differently, in more compact way, as we did it in the class. Combine the top three decision nodes in one node, where both players make their decision simultaneously. (b) How many subgames are in this game? What is the length of the game? (c) What is Amy's strategy set? Bob's? (d) Find the subgame perfect equilibrium strategies, the equilibrium path and the equilibrium payoffs of the players in the equilibrium. Explain how you arrived to this equilibrium. (e) Since Bob's best payoff in this game is 8, how can he credibly threaten Amy to get the outcome with payoff of 8? Explain. (0 Construct strategic form of this game. Find all Nash equilibia and discuss whether they are Pareto optimal. Indicate which of them is the subgameperfect equilibrium (equilibria)