Question 2. In an industry, there is an incumbent firm (Firm 1) and there is a potential entrant firm (Firm 2). Firm 1 decides whether to build a new plant, and simultaneously Firm 2 decides whether to enter into this industry. The cost of building a new plant for Firm 1 can be high or low, which is Firm l's private information. Firm 2 is uncertain about Firm 1's cost, and believes that with probability TE [0, 1] the building cost for Firm 1 is high, and low with probability 1-7. The payoffs are depicted below. Build Not Build Enter 0, -1 2,1 Not Enter 2,0 3,0 High Cost = H) = π, and P(0₁ Build Not Build This interaction comprise a Bayesian game. Firm 2 does not know the matrix in which they are in, but Firm 1 does now it. As we have seen in class, there are 5 things that define this Bayesian game. 1. Set of players: N = {Firm 1, Firm 2}. 2. Set of actions for each player: A₁ = {Build, Not Build}, A2 = {Enter, Not Enter}. 3. Type space of Firm 1: ₁ = {H, L}. 1 = Enter 1.5, -1 2,1 4. Payoff functions: v₂: A₁ x A₂ × ₁ → R for each i E N, which are defined in the above matrices. 5. Common prior: P(01 Not Enter 3.5,0 3,0 L) = 1 - T. Low Cost Let (q, q,p*) be a Bayesian Nash equilibrium of this game, where q € [0, 1] is the probability that a 0 € ₁ type Firm 1 builds the plant, and p* is the probability that Firm 2 enters into industry. Characterize all Bayesian Nash equilibria for each belief .
Question 2. In an industry, there is an incumbent firm (Firm 1) and there is a potential entrant firm (Firm 2). Firm 1 decides whether to build a new plant, and simultaneously Firm 2 decides whether to enter into this industry. The cost of building a new plant for Firm 1 can be high or low, which is Firm l's private information. Firm 2 is uncertain about Firm 1's cost, and believes that with probability TE [0, 1] the building cost for Firm 1 is high, and low with probability 1-7. The payoffs are depicted below. Build Not Build Enter 0, -1 2,1 Not Enter 2,0 3,0 High Cost = H) = π, and P(0₁ Build Not Build This interaction comprise a Bayesian game. Firm 2 does not know the matrix in which they are in, but Firm 1 does now it. As we have seen in class, there are 5 things that define this Bayesian game. 1. Set of players: N = {Firm 1, Firm 2}. 2. Set of actions for each player: A₁ = {Build, Not Build}, A2 = {Enter, Not Enter}. 3. Type space of Firm 1: ₁ = {H, L}. 1 = Enter 1.5, -1 2,1 4. Payoff functions: v₂: A₁ x A₂ × ₁ → R for each i E N, which are defined in the above matrices. 5. Common prior: P(01 Not Enter 3.5,0 3,0 L) = 1 - T. Low Cost Let (q, q,p*) be a Bayesian Nash equilibrium of this game, where q € [0, 1] is the probability that a 0 € ₁ type Firm 1 builds the plant, and p* is the probability that Firm 2 enters into industry. Characterize all Bayesian Nash equilibria for each belief .
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![Question 2. In an industry, there is an incumbent firm (Firm 1) and there is a potential entrant firm
(Firm 2). Firm 1 decides whether to build a new plant, and simultaneously Firm 2 decides whether to
enter into this industry. The cost of building a new plant for Firm 1 can be high or low, which is Firm
1's private information. Firm 2 is uncertain about Firm 1's cost, and believes that with probability
TE [0, 1] the building cost for Firm 1 is high, and low with probability 1-7. The payoffs are depicted
below.
Build
Not Build
Enter
0, -1
2,1
Not Enter
2,0
3,0
High Cost
Build
Not Build
1
Enter
1.5, -1
2,1
Not Enter
3.5,0
3,0
Low Cost
This interaction comprise a Bayesian game. Firm 2 does not know the matrix in which they are in,
but Firm 1 does now it.
As we have seen in class, there are 5 things that define this Bayesian game.
1. Set of players: N {Firm 1, Firm 2}.
=
2. Set of actions for each player: A₁ = {Build, Not Build}, A2
3. Type space of Firm 1: ₁ = {H, L}.
{Enter, Not Enter}.
4. Payoff functions: v₂ : A₁ × A₂ × ₁ → R for each i EN, which are defined in the above matrices.
5. Common prior: P(0₁ = H) =
= π, and P(0₁ L) = 1 - T.
Let (q, q,p*) be a Bayesian Nash equilibrium of this game, where q = [0, 1] is the probability that
₁ type Firm 1 builds the plant, and p* is the probability that Firm 2 enters into industry.
Characterize all Bayesian Nash equilibria for each belief .
a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb6084007-80ef-4953-ac4a-29df291b4d04%2Fdaf5b525-77a9-4751-a340-40ad1f953ccc%2Fpmml7xv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 2. In an industry, there is an incumbent firm (Firm 1) and there is a potential entrant firm
(Firm 2). Firm 1 decides whether to build a new plant, and simultaneously Firm 2 decides whether to
enter into this industry. The cost of building a new plant for Firm 1 can be high or low, which is Firm
1's private information. Firm 2 is uncertain about Firm 1's cost, and believes that with probability
TE [0, 1] the building cost for Firm 1 is high, and low with probability 1-7. The payoffs are depicted
below.
Build
Not Build
Enter
0, -1
2,1
Not Enter
2,0
3,0
High Cost
Build
Not Build
1
Enter
1.5, -1
2,1
Not Enter
3.5,0
3,0
Low Cost
This interaction comprise a Bayesian game. Firm 2 does not know the matrix in which they are in,
but Firm 1 does now it.
As we have seen in class, there are 5 things that define this Bayesian game.
1. Set of players: N {Firm 1, Firm 2}.
=
2. Set of actions for each player: A₁ = {Build, Not Build}, A2
3. Type space of Firm 1: ₁ = {H, L}.
{Enter, Not Enter}.
4. Payoff functions: v₂ : A₁ × A₂ × ₁ → R for each i EN, which are defined in the above matrices.
5. Common prior: P(0₁ = H) =
= π, and P(0₁ L) = 1 - T.
Let (q, q,p*) be a Bayesian Nash equilibrium of this game, where q = [0, 1] is the probability that
₁ type Firm 1 builds the plant, and p* is the probability that Firm 2 enters into industry.
Characterize all Bayesian Nash equilibria for each belief .
a
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education