Consider the following game, where the payoffs are given in the following order (from top to bottom): Player 1, Player 2, Player 3. 6 0 0 2 0 0 4 2 6 4 0 0 y 5 4 Note: to answer the following questions you don't need to write the normal form (you will save a lot of time 1f you reason on the extensive form without constructing the normal form). (a) Are there values of x for which Player | has a strictly dominant strategy? If your answer 1s Yes, say what values and what strategy, if your answer 1s No explain why not. (b) Are there values of y for which Player 3 has a strictly dominant strategy? If your answer 1s Yes, say what values and what strategy, 1f your answer 1s No explain why not. () Does Player 2 have weakly dominated strategies? (If your answer 1s Yes, name the strategies and the strategies that dominate them; if your answer 1s No prove your claim.) (d) For what values of y does Player 3 have a weakly dominated strategy? Name the strategy. () How many strategies does Player 2 have? () Find all the backward-induction solutions when x = 1 and y = 27 (g2) Find the backward-induction solution whenx =1 and y = 3. (h) [4 points] Assume that x = | and y = 1. Explain why (8,D,L) 1s not a Nash equilibrium. (i) Assume that x =1 and y = 1. Explain why (8,D,L) is not a backward-induction solution. (j) Assume that x =1 and y = 1. Is there a Nash equilibrium where Player 1 plays A? If Yes, then say what the equilibrium 1s, 1f No then explain why not. Q1.1 (a) 1 Point Are there values of x for which Player 1 has a strictly dominant strategy? If your answer is Yes, what values and what strategy? O any x > 6, A O any x 6, C O any x 2, B O No, there's no strictly dominant strategy for player 1 regardless of xQ1.2 (b) 1 Point Are there values of y for which Player 3 has a strictly dominant strategy? If your answer is Yes, say what values and what strateqgy? (0 No, there's no strictly dominant strategy for player 3 regardless of y (O any y > 2, given player 1 plays B and player 2 plays D, play H (O any y > 4, given player 1 plays B and player 2 plays D, play L @ any y 0 Oy 2 Oy # 2 Oy> 4 Oy# 4 Oy