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A particular three player game

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Reference no: EM131252272

Suppose you know the following for a particular three-player game: The space of strategy profiles S is finite. Also, for every s ∈ S, it is the case that

u2(S)= 3u1(S), u3(S) = [u1(S)]2, and u1(S)€ [0,1].

(a) Must this game have a Nash equilibrium? Explain your answer.

(b) Must this game have an efficient Nash equilibrium? Explain your answer.

(c) Suppose that in addition to the information given above, you know that s* is a Nash equilibrium of the game. Must s* be an efficient strategy profile? Explain your answer; if you answer "no," then provide a counterexample.

Reference no: EM131252272

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