Suppose you know the following for a particular, Game Theory

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Suppose you know the following for a particular

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.

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