2. Consider the following Bayesian game with two players. Both players move simultaneously and player 1 can choose either H or L, while player 2's options are G, M, and D. With probability 1/2 the payoffs are given by "Game 1" : D H 1,2 1,0 1,3 L 2,4 0,0 0,5 and with probability 1/2 the payoffs are according to "Game 2": GMD H 1,2 1,3 1,0 L 2,4 0,5 0,0 (a) Find the Nash Equilibria when neither player knows which game is actually played. (b) Assume now that player 2 knows which one among the two games is actually being played. Check that the game has a unique Bayesian Nash Equilibrium.
2. Consider the following Bayesian game with two players. Both players move simultaneously and player 1 can choose either H or L, while player 2's options are G, M, and D. With probability 1/2 the payoffs are given by "Game 1" : D H 1,2 1,0 1,3 L 2,4 0,0 0,5 and with probability 1/2 the payoffs are according to "Game 2": GMD H 1,2 1,3 1,0 L 2,4 0,5 0,0 (a) Find the Nash Equilibria when neither player knows which game is actually played. (b) Assume now that player 2 knows which one among the two games is actually being played. Check that the game has a unique Bayesian Nash Equilibrium.
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.3P
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Question
![2. Consider the following Bayesian game with two players. Both players move simultaneously and player 1 can choose
either H or L, while player 2's options are G, M, and D. With probability 1/2 the payoffs are given by "Game 1" :
GMD
H
1,2
1,0
1,3
L 2,4 0,0 0,5
and with probability 1/2 the payoffs are according to "Game 2" :
G
|M|D
H
1,2 1,3 1,0
L
2,4 0,5 0,0
(a) Find the Nash Equilibria when neither player knows which game is actually played.
(b) Assume now that player 2 knows which one among the two games is actually being played. Check that the game
has a unique Bayesian Nash Equilibrium.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbf8ee92f-ba39-4be8-985d-aa9c69d8e21c%2F85e99c19-8bc5-4406-bdce-92f7786539d4%2Fz3lyos_processed.png&w=3840&q=75)
Transcribed Image Text:2. Consider the following Bayesian game with two players. Both players move simultaneously and player 1 can choose
either H or L, while player 2's options are G, M, and D. With probability 1/2 the payoffs are given by "Game 1" :
GMD
H
1,2
1,0
1,3
L 2,4 0,0 0,5
and with probability 1/2 the payoffs are according to "Game 2" :
G
|M|D
H
1,2 1,3 1,0
L
2,4 0,5 0,0
(a) Find the Nash Equilibria when neither player knows which game is actually played.
(b) Assume now that player 2 knows which one among the two games is actually being played. Check that the game
has a unique Bayesian Nash Equilibrium.
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