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Please solve (show your solution). 1. Enumerate all pure strategies for each player. 2. Suppose that player 1 observes his type ?1 = 3. How does player 1 think of the probability of ?2? 3. Find a (pure strategy) Bayesian Nash equilibrium.

Please solve (show your solution). 1. Enumerate all pure strategies for each player. 2. Suppose that player 1 observes his type ?1 = 3. How does player 1 think of the probability of ?2? 3. Find a (pure strategy) Bayesian Nash equilibrium.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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E3

 

Bayesian Game]. Consider a Bayesian game described by a following payoff matrix.

 

Please solve (show your solution).

1. Enumerate all pure strategies for each player.

2. Suppose that player 1 observes his type ?1 = 3. How does player 1 think of the probability of ?2?

3. Find a (pure strategy) Bayesian Nash equilibrium.

Consider a Bayesian game described by a following payoff matrix. 1 / 2 A B A B 4 4, 0₂ 2, 2 i For each i E {1,2}, 0; takes either 0 or 3 (0 € {0,3}). Values of 0; (i = 1,2) is private information of player i. State of the world (0₁,0₂) is distributed by a following probability distribution. 0₁ + 0₂, 0₁ / 0₂ 1 0 3 0₁+0₂ 0 1/2 1/10 012 3 1/10 3/10
Transcribed Image Text:Consider a Bayesian game described by a following payoff matrix. 1 / 2 A B A B 4 4, 0₂ 2, 2 i For each i E {1,2}, 0; takes either 0 or 3 (0 € {0,3}). Values of 0; (i = 1,2) is private information of player i. State of the world (0₁,0₂) is distributed by a following probability distribution. 0₁ + 0₂, 0₁ / 0₂ 1 0 3 0₁+0₂ 0 1/2 1/10 012 3 1/10 3/10
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