[Game Theory} ECN
Consider the following extensive game, where the payoffs aregiven in the following order, from left to right: (player 1, player2, player 3).
Game Theory Ecn Consider The Following Extensive Game Where The Payoffs Are Given In The Following Order From Left T 1 (36.25 KiB) Viewed 26 times
(a) Are there values of x for which Player 1 has a strictlydominant strategy? If your answer is Yes, say what values and whatstrategy, if your answer is No explain why not.(b) Are there values of y for which Player 3 has a strictlydominant strategy? If your answer is Yes, say what values and whatstrategy, if your answer is No explain why not.(c) Does Player 2 have weakly dominated strategies? (If your answeris 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 dominatedstrategy? 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 wherePlayer 1 plays C? If Yes, then say what the equilibrium is, if Nothen explain why not.
(x, 4, 8) C F (0, 4,0) 2 B G 1 (8,0,5) H A (2,6,2) 3 D L 2 E (0, 4, 4) (0, 2, y)
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