Suppose you know the following about a particular two-player game: S = {A, B, C), S...

 

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Suppose you know the following about a particular two-player game: S₁ = {A, B, C), S₂ = (X, Y, Z}, u₁(A, X) = 6, u, (A, Y) = 0, and u, (A, Z) = 0. In addition, suppose you know that the game has a mixed-strategy Nash equilibrium in which (a) the players select each of their strategies with posi- tive probability, (b) player 1's expected payoff in equilibrium is 4, and (c) player 2's expected payoff in equilibrium is 6. Do you have enough infor- mation to calculate the probability that player 2 selects X in equilibrium? If so, what is this probability? Suppose you know the following about a particular two-player game: S₁ = {A, B, C), S₂ = (X, Y, Z}, u₁(A, X) = 6, u, (A, Y) = 0, and u, (A, Z) = 0. In addition, suppose you know that the game has a mixed-strategy Nash equilibrium in which (a) the players select each of their strategies with posi- tive probability, (b) player 1's expected payoff in equilibrium is 4, and (c) player 2's expected payoff in equilibrium is 6. Do you have enough infor- mation to calculate the probability that player 2 selects X in equilibrium? If so, what is this probability?