Problem 1. Consider the following extensive form game with three players, player 1, player 2, and player 3. The payoffs are listed in the usual way, so that (p1. P2, P3) means p is the payoff to player 1, p2 is the payoff to player 2, and p3 is the payoff to player 3. (a) For each player i, determine the size of the strategy set S,. You do not need to list the strategies in cach sot. (b) For player 3 describe in words what is meant by the strategy s3 = b. (c) Use backward induction to analyze the game. Indicate the path of play that will be taken according to your analysis. (d) Identify at least one outcome that all players would prefer over the outcome reached through the backward induction analysis. (e) Are there threats or promises that players could make that would lead to this preferred outcome? Assume that players will act on threats or promises made if the path of play reaches the node where the threat or promise applies and show that the threat or promise satisfies the definition given in the lecture. Y (30,5,0) (0,6,2) (20,3,3) (-1,20, 1) (-2,8, 10) (10, 12, 8) (12,5,7) (8,-2,3) (5, 10,5) (6,12,8) I Y 2 (10,6,5) (7,-5, 15) (4,15,2). b