6) Consider the following signaling game:20, 50,010, -10-10,0LeftLeftRightRightPlayer 2Player 21-aUpUpNaturePlayer 1-APlayer 1-BТуре А — 50%Туре В — 50%DownDownPlayer 21-BPlayer 2LeftRightLeftRight10,50,05, -100,0Let's see if it has a pooling equilibrium. Follow the following steps:a. Specify strategies of a possible pooling equilibriumb. Determine player 2’s on-path beliefs for the belief probabilities a and ß asappropriate. You can infer these beliefs from what we know about beliefs inpooling equilibria, and do not havefully calculate them.c. Check whether either player wants to deviate. Is there a pooling equilibrium?d. Determine the off-path beliefs that make the equilibrium hold.

For the Above signaling game following steps are taken : Player 1 is chosen by nature to make…

6) Consider the following signaling game: 20, 5 0,0 10, -10 -10,0 Left Right Left Right Player 2 Player 2 1-a a Up Up Nature Player 1-A Player 1-B Туре А — 50% Туре В - 50% Down Down B Player 2 1-B Player 2 Left Right Left Right 10,5 0,0 5, -10 0,0

6) Consider the following signaling game: 20, 5 0,0 10, -10 -10,0 Left Right Left Right Player 2 Player 2 1-a a Up Up Nature Player 1-A Player 1-B Туре А — 50% Туре В - 50% Down Down B Player 2 1-B Player 2 Left Right Left Right 10,5 0,0 5, -10 0,0

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.9P

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Question

6) Consider the following signaling game:
20, 5
0,0
10, -10
-10,0
Left
Left
Right
Right
Player 2
Player 2
1-a
Up
Up
Nature
Player 1-A
Player 1-B
Туре А — 50%
Туре В — 50%
Down
Down
Player 2
1-B
Player 2
Left
Right
Left
Right
10,5
0,0
5, -10
0,0
Let's see if it has a pooling equilibrium. Follow the following steps:
a. Specify strategies of a possible pooling equilibrium
b. Determine player 2’s on-path beliefs for the belief probabilities a and ß as
appropriate. You can infer these beliefs from what we know about beliefs in
pooling equilibria, and do not have
fully calculate them.
c. Check whether either player wants to deviate. Is there a pooling equilibrium?
d. Determine the off-path beliefs that make the equilibrium hold.

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