Let G be the following static game. Rose Colin A B A (3,4) (1,5) B (4,2) (0,1) (a) Determine the pure Nash equilibria of G. (b) Rose A, B, Colin A, B is a mixed Nash equilibrium of H. (You do not have to verify this.) Determine the expected payoffs of both players given that they choose their strategies according to this Nash equilibrium. (c) Draw the payoff polygon of H. Indicate on your diagram the points corresponding to the Nash equilibria of H, and the points corresponding to Pareto optimal solu- tions of H.
Let G be the following static game. Rose Colin A B A (3,4) (1,5) B (4,2) (0,1) (a) Determine the pure Nash equilibria of G. (b) Rose A, B, Colin A, B is a mixed Nash equilibrium of H. (You do not have to verify this.) Determine the expected payoffs of both players given that they choose their strategies according to this Nash equilibrium. (c) Draw the payoff polygon of H. Indicate on your diagram the points corresponding to the Nash equilibria of H, and the points corresponding to Pareto optimal solu- tions of H.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Step 1
Given
Game matrix
Colin | |||
A | B | ||
Rose | A | (3,4) | (1,5) |
B | (4,2) | (0,1) |
To find pure strategies Nash-equilibria, we will find the best response for Rose and Colin. The intersection of the best response will be the pure strategies Nash equilibria.
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