HOMEWORK 10: GAME THEORY ASSIGNMENT 5 Player 2 X Y Question 1. Consider the following game: Player 1 A -1, -2 -1, 2 B -2, 2 2, -2 Q1)a) Suppose Player 1 is using a mixed strategy, and they chooses strategy A one third of the time. What are the expected payoffs for each of Player 2's strategies? Expected payoff for strategy X, Ez(X) = . . . Expected payoff for strategy Y, E2(Y) = . .. Q1)b) Suppose Player 1 is using a mixed strategy, and they chooses strategy A with probability p. Write formulas for the expected payoffs of each of Player 2's strategies. Expected payoff for strategy X, E2(X) = Expected payoff for strategy Y, E2(Y) = Q1)c) What value of p makes Player 2's expected payoffs the same for both of their strategies? (This is called Player 1's indifference strategy.) Q1)d) Suppose Player 2 is also using a mixed strategy, and plays strategy X with probability q. Write formulas for the expected payoffs of each of Player 1's strategies. Expected payoff for strategy A, E1 (A) = . . . . Expected payoff for strategy B, El(B) = Q1)e) What value of q makes Player 1's expected payoffs the same for both of their strategies? (This is called Player 2's indifference strategy.) Q1)f) Calculate any Mixed Nash Equilibrium: Q1)g) At the mixed-strategy Nash Equilibrium, calculate the expected payoff to each player. Expected Payoff for Player 1: ......... Expected payoff for Player 2