Suppose you know the following about a particular two-player game: S1 = {A, B, C}, S2 = {X, Y, Z}, u1(A, X) = 6, u1(A, Y) = 0, and u1(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 positive 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 information to calculate the probability that player 2 selects X in equilibrium? If so, what is this probability?