4. An incumbent chain store faces two different entrants E₁ (in the first market) and E2 (in the second market). The incumbent can choose to accommodate (A) or fight (F) in the first market. The second entrant E2 observes the outcome of first interaction before deciding whether to enter the second market (I) or stay out (O). Incumbent could be tough, wo. Other incumbent is normal, wn. In the second market, normal incumbent accommodates and tough fights. Conditional on entry in the first market, the resulting signaling game played between the incumbent and E2 is illustrated below. In the signaling game, Nature chooses the incumbent to be tough with probability . UI,UE UI,UE 4,-1 I' [P] F wo A [9] I 3,-1 6,0 O' Tough [2/3] 5,0 E2 E2 3,1 I' Normal [1/3] 4,1 1-p] F' Wn A'[1-9 5,0 6,0 (a) List out all of the strategies for the incumbent and E2. (b) Is there a separating perfect Bayesian equilibrium? If so, find all the separating perfect Bayesian equilibria. If not, briefly demonstrate why. (c) Is there a pooling perfect Bayesian equilibrium in which both types of incumbents fight in the first market? If so, find all such pooling perfect Bayesian equilibria. If not, briefly demonstrate why.
4. An incumbent chain store faces two different entrants E₁ (in the first market) and E2 (in the second market). The incumbent can choose to accommodate (A) or fight (F) in the first market. The second entrant E2 observes the outcome of first interaction before deciding whether to enter the second market (I) or stay out (O). Incumbent could be tough, wo. Other incumbent is normal, wn. In the second market, normal incumbent accommodates and tough fights. Conditional on entry in the first market, the resulting signaling game played between the incumbent and E2 is illustrated below. In the signaling game, Nature chooses the incumbent to be tough with probability . UI,UE UI,UE 4,-1 I' [P] F wo A [9] I 3,-1 6,0 O' Tough [2/3] 5,0 E2 E2 3,1 I' Normal [1/3] 4,1 1-p] F' Wn A'[1-9 5,0 6,0 (a) List out all of the strategies for the incumbent and E2. (b) Is there a separating perfect Bayesian equilibrium? If so, find all the separating perfect Bayesian equilibria. If not, briefly demonstrate why. (c) Is there a pooling perfect Bayesian equilibrium in which both types of incumbents fight in the first market? If so, find all such pooling perfect Bayesian equilibria. If not, briefly demonstrate why.
Principles of Microeconomics (MindTap Course List)
8th Edition
ISBN:9781305971493
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter17: Oligopoly
Section: Chapter Questions
Problem 9PA
Related questions
Question
![4. An incumbent chain store faces two different entrants E₁ (in the first market) and E2 (in
the second market). The incumbent can choose to accommodate (A) or fight (F) in the first
market. The second entrant E2 observes the outcome of first interaction before deciding
whether to enter the second market (I) or stay out (O). Incumbent could be tough, wo.
Other incumbent is normal, wn. In the second market, normal incumbent accommodates
and tough fights. Conditional on entry in the first market, the resulting signaling game
played between the incumbent and E2 is illustrated below. In the signaling game, Nature
chooses the incumbent to be tough with probability .
UI,UE
UI,UE
4,-1
I'
[P] F wo A [9]
I
3,-1
6,0
O'
Tough [2/3]
5,0
E2
E2
3,1
I'
Normal [1/3]
4,1
1-p] F' Wn A'[1-9
5,0
6,0
(a) List out all of the strategies for the incumbent and E2.
(b) Is there a separating perfect Bayesian equilibrium? If so, find all the separating
perfect Bayesian equilibria. If not, briefly demonstrate why.
(c) Is there a pooling perfect Bayesian equilibrium in which both types of incumbents
fight in the first market? If so, find all such pooling perfect Bayesian equilibria. If
not, briefly demonstrate why.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18f59e4c-f790-4f63-be0e-73ac48e946b6%2Fca0510a1-b0da-4283-949a-851078f41745%2Fx26unuc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. An incumbent chain store faces two different entrants E₁ (in the first market) and E2 (in
the second market). The incumbent can choose to accommodate (A) or fight (F) in the first
market. The second entrant E2 observes the outcome of first interaction before deciding
whether to enter the second market (I) or stay out (O). Incumbent could be tough, wo.
Other incumbent is normal, wn. In the second market, normal incumbent accommodates
and tough fights. Conditional on entry in the first market, the resulting signaling game
played between the incumbent and E2 is illustrated below. In the signaling game, Nature
chooses the incumbent to be tough with probability .
UI,UE
UI,UE
4,-1
I'
[P] F wo A [9]
I
3,-1
6,0
O'
Tough [2/3]
5,0
E2
E2
3,1
I'
Normal [1/3]
4,1
1-p] F' Wn A'[1-9
5,0
6,0
(a) List out all of the strategies for the incumbent and E2.
(b) Is there a separating perfect Bayesian equilibrium? If so, find all the separating
perfect Bayesian equilibria. If not, briefly demonstrate why.
(c) Is there a pooling perfect Bayesian equilibrium in which both types of incumbents
fight in the first market? If so, find all such pooling perfect Bayesian equilibria. If
not, briefly demonstrate why.
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