Consider Bernard \ Mary Left Center Right Top 0,5 1,0 2,2 Bottom 1,0 0,3 2,2 The first number in a cell denotes the payoff to Bernard and the second number denotes the payoff to MaryForexample: πB(B,L)=1and πM(T,L)=5. a  Give all pure strategy Nash equilibria of this one-shot game, if any. Briefly explain. Let Bernard play Top with probability p and Bottom with probability 1 − p; let Mary play Left with probability qL , Center with probability qC and Right with probability qR = 1 − qL − qC . b Give all mixed strategy Nash equilibria of this game.

Microeconomic Theory
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Chapter8: Game Theory
Section: Chapter Questions
Problem 8.1P
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Consider

Bernard \ Mary Left Center Right
Top 0,5 1,0 2,2
Bottom 1,0 0,3 2,2

The first number in a cell denotes the payoff to Bernard and the second number denotes the payoff to MaryForexample: πB(B,L)=1and πM(T,L)=5.

a  Give all pure strategy Nash equilibria of this one-shot game, if any. Briefly explain.
Let Bernard play Top with probability p and Bottom with probability 1 − p; let Mary play Left with probability qL , Center with probability qC and Right with probability qR = 1 − qL − qC .

b Give all mixed strategy Nash equilibria of this game.

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