2- Consider the following game. Player 2 LR Player 1 U 12, 2 3,9 | D 5, 8 4, 2 (a) Find all the Nash equilibria, pure and mixed. (b) Suppose that the payoff of the column player u:(D, L) is reduced from 8 to 6, but all other navoffs remain the same Again find all the nure, and mixed-strategy Nash cauilibria

Microeconomic Theory
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Chapter8: Game Theory
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Problem 8.1P
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2- Consider the following game.
Player 2
Player 1 U 12, 2 | 3, 9
5, 8 4, 2
D
(a) Find all the Nash equilibria, pure and mixed.
(b) Suppose that the payoff of the column player u:(D, L) is reduced from 8 to 6, but all other
payoffs remain the same. Again, find all the pure- and mixed-strategy Nash equilibria.
(c) Compare the mixed-strategy equilibria in parts (a) and (b). Did this worsening in one of player 2's
payoffs change player 2's equilibrium mixed strategy? Did it change player l's? Give some intuition.
Transcribed Image Text:2- Consider the following game. Player 2 Player 1 U 12, 2 | 3, 9 5, 8 4, 2 D (a) Find all the Nash equilibria, pure and mixed. (b) Suppose that the payoff of the column player u:(D, L) is reduced from 8 to 6, but all other payoffs remain the same. Again, find all the pure- and mixed-strategy Nash equilibria. (c) Compare the mixed-strategy equilibria in parts (a) and (b). Did this worsening in one of player 2's payoffs change player 2's equilibrium mixed strategy? Did it change player l's? Give some intuition.
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