In the above game, explain in words what condition player 1's probability p of playing strategy A must satisfy to induce player 2 to mix strategies between a and b in equilibrium. Solve for the mixed strategy Nash equilibrium where player 1 chooses A with probability P and player 2 chooses a with probability p, for 0 < p, P < 1.

Microeconomic Theory
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Chapter8: Game Theory
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5) Mixed strategy Nash equilibrium
Consider a mixed strategy Nash equilibrium of the following coordination game:
Player 2
Player 1
A
B
a
5.5
6.-2
b
-2,6
1,1
a) In the above game, explain in words what condition player 1's probability p of playing
strategy A must satisfy to induce player 2 to mix strategies between a and b in
equilibrium.
b) Solve for the mixed strategy Nash equilibrium where player 1 chooses A with
probability P and player 2 chooses a with probability p, for 0 < p, P < 1.
Transcribed Image Text:5) Mixed strategy Nash equilibrium Consider a mixed strategy Nash equilibrium of the following coordination game: Player 2 Player 1 A B a 5.5 6.-2 b -2,6 1,1 a) In the above game, explain in words what condition player 1's probability p of playing strategy A must satisfy to induce player 2 to mix strategies between a and b in equilibrium. b) Solve for the mixed strategy Nash equilibrium where player 1 chooses A with probability P and player 2 chooses a with probability p, for 0 < p, P < 1.
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