Consider the following extensive game, where the payoffs are given in the following order, from left to right: (player 1, player 2, player 3). C (1, 4, 8) B A 2 D E G 3 (0, 4,0) (8, 0,5) (0, 4, 4) H L (2, 6, 2) (0, 2, y) (a) Are there values of x for which Player 1 has a strictly dominant strat- egy? If your answer is Yes, say what values and what strategy, if your answer is No explain why not. (b) Are there values of y for which Player 3 has a strictly dominant strat- egy? If your answer is Yes, say what values and what strategy, if your answer is No explain why not. (c) Does Player 2 have weakly dominated strategies? (If your answer is Yes, name the strategies and the strategies that dominate them; if your answer is No prove your claim.) (d) For what values of y does Player 3 have a weakly dominated strategy? Name the strategy. (e) How many strategies does Player 2 have? (f) Find all the backward induction solutions when x = 1 and y = 2. (g) Find the backward-induction solution when x = 1 and y = 3. (h) Assume that x = 1 and y = 1. Is there a Nash equilibrium where Player 1 plays C? If Yes, then say what the equilibrium is, if No then explain why not