Consider now a Bertrand competition environment with one good and two firms, Firm 1 and Firm 2. The (pure) strategy space of Firm 1 is S₁ = [0,5], and the strategy s₁ of Firm 1 corresponds to the price they charge for the good. Similarly, the (pure) strategy space of Firm 2 is S₂ = [0,5], and the strategy s2 of Firm 2 corresponds to the price they charge for the good. If Firm 1 were to choose price s₁ and Firm 2 were to choose price s2, then the demand Firm 1 would face is given by if 81 < 82, if 81 = 82, 0 if 81 > 82, D1(81, 82) = the demand Firm 2 would face is given by 1 if 82 < $1, D2($1, $2) 2 if 82 = 81, 0 if 82 > 81, the utility of Firm 1 would be their profit, u₁($1,82) = (81 − 1)D₁(81, 82), and the utility of Firm 2 would be their profit, u2($1, $2) = (82 − 1)D2(81, 82). (The marginal cost of production for both firms is 1.) (c) Find the pure-strategy Nash equilibria of this game. Consider now an altered version of the Bertrand competition environment above in which the (pure) strategy space of Firm 1 is S₁ = {0,1,2,3,4,5}, the (pure) strategy space of Firm 2 is S2 = {0, 1, 2, 3, 4, 5}, and otherwise the game is the same as the Bertrand competition environment above. (d) Find the pure-strategy Nash equilibria of this game. = 2. Consider a Cournot competition environment with one good and two firms, Firm 1 and Firm 2. The (pure) strategy space of Firm 1 is S₁ [0, 1], and the strategy s₁ of Firm 1 corresponds to the amount of the good they produce. Similarly, the (pure) strategy space of Firm 2 is S₂ = [0, 1], and the strategy 82 of Firm 2 corresponds to the amount of the good they produce. If Firm 1 were to produce quantity 8₁ and Firm 2 were to produce quantity 82, the prevailing price in the good market would be 1-81-82, the utility of Firm 1 would be their profit, u₁ ($1, $2) = (1 - 81 - 82 - c)s1, and the utility of Firm 2 would be their profit, u2($1, $2) = (1-81-82-c)s2, where 0 ≤ c < 1 is the marginal cost of production for both firms. (a) Find the pure-strategy Nash equilibria of this game. (b) Are there other Nash equilibria in this game.
Consider now a Bertrand competition environment with one good and two firms, Firm 1 and Firm 2. The (pure) strategy space of Firm 1 is S₁ = [0,5], and the strategy s₁ of Firm 1 corresponds to the price they charge for the good. Similarly, the (pure) strategy space of Firm 2 is S₂ = [0,5], and the strategy s2 of Firm 2 corresponds to the price they charge for the good. If Firm 1 were to choose price s₁ and Firm 2 were to choose price s2, then the demand Firm 1 would face is given by if 81 < 82, if 81 = 82, 0 if 81 > 82, D1(81, 82) = the demand Firm 2 would face is given by 1 if 82 < $1, D2($1, $2) 2 if 82 = 81, 0 if 82 > 81, the utility of Firm 1 would be their profit, u₁($1,82) = (81 − 1)D₁(81, 82), and the utility of Firm 2 would be their profit, u2($1, $2) = (82 − 1)D2(81, 82). (The marginal cost of production for both firms is 1.) (c) Find the pure-strategy Nash equilibria of this game. Consider now an altered version of the Bertrand competition environment above in which the (pure) strategy space of Firm 1 is S₁ = {0,1,2,3,4,5}, the (pure) strategy space of Firm 2 is S2 = {0, 1, 2, 3, 4, 5}, and otherwise the game is the same as the Bertrand competition environment above. (d) Find the pure-strategy Nash equilibria of this game. = 2. Consider a Cournot competition environment with one good and two firms, Firm 1 and Firm 2. The (pure) strategy space of Firm 1 is S₁ [0, 1], and the strategy s₁ of Firm 1 corresponds to the amount of the good they produce. Similarly, the (pure) strategy space of Firm 2 is S₂ = [0, 1], and the strategy 82 of Firm 2 corresponds to the amount of the good they produce. If Firm 1 were to produce quantity 8₁ and Firm 2 were to produce quantity 82, the prevailing price in the good market would be 1-81-82, the utility of Firm 1 would be their profit, u₁ ($1, $2) = (1 - 81 - 82 - c)s1, and the utility of Firm 2 would be their profit, u2($1, $2) = (1-81-82-c)s2, where 0 ≤ c < 1 is the marginal cost of production for both firms. (a) Find the pure-strategy Nash equilibria of this game. (b) Are there other Nash equilibria in this game.
Chapter15: Imperfect Competition
Section: Chapter Questions
Problem 15.8P
Related questions
Question
What are the answers for a,b,c,d? Are they supposed to be numerical answers or in terms of a variable?
![Consider now a Bertrand competition environment with one good and two firms, Firm 1 and Firm 2.
The (pure) strategy space of Firm 1 is S₁ = [0,5], and the strategy s₁ of Firm 1 corresponds to the
price they charge for the good. Similarly, the (pure) strategy space of Firm 2 is S₂ = [0,5], and the
strategy s2 of Firm 2 corresponds to the price they charge for the good. If Firm 1 were to choose price
s₁ and Firm 2 were to choose price s2, then the demand Firm 1 would face is given by
if 81 < 82,
if 81 = 82,
0 if 81 > 82,
D1(81, 82)
=
the demand Firm 2 would face is given by
1
if 82 < $1,
D2($1, $2)
2
if 82 = 81,
0
if 82 > 81,
the utility of Firm 1 would be their profit, u₁($1,82) = (81 − 1)D₁(81, 82), and the utility of Firm 2
would be their profit, u2($1, $2) = (82 − 1)D2(81, 82). (The marginal cost of production for both firms
is 1.)
(c) Find the pure-strategy Nash equilibria of this game.
Consider now an altered version of the Bertrand competition environment above in which the (pure)
strategy space of Firm 1 is S₁ = {0,1,2,3,4,5}, the (pure) strategy space of Firm 2 is S2 = {0, 1, 2, 3, 4, 5},
and otherwise the game is the same as the Bertrand competition environment above.
(d) Find the pure-strategy Nash equilibria of this game.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F939ffa75-c788-435b-b74a-4ee3a4182c06%2Fd51afac1-1ef8-4dce-b4e5-545eb08b29f4%2Fohcejnj_processed.png&w=3840&q=75)
Transcribed Image Text:Consider now a Bertrand competition environment with one good and two firms, Firm 1 and Firm 2.
The (pure) strategy space of Firm 1 is S₁ = [0,5], and the strategy s₁ of Firm 1 corresponds to the
price they charge for the good. Similarly, the (pure) strategy space of Firm 2 is S₂ = [0,5], and the
strategy s2 of Firm 2 corresponds to the price they charge for the good. If Firm 1 were to choose price
s₁ and Firm 2 were to choose price s2, then the demand Firm 1 would face is given by
if 81 < 82,
if 81 = 82,
0 if 81 > 82,
D1(81, 82)
=
the demand Firm 2 would face is given by
1
if 82 < $1,
D2($1, $2)
2
if 82 = 81,
0
if 82 > 81,
the utility of Firm 1 would be their profit, u₁($1,82) = (81 − 1)D₁(81, 82), and the utility of Firm 2
would be their profit, u2($1, $2) = (82 − 1)D2(81, 82). (The marginal cost of production for both firms
is 1.)
(c) Find the pure-strategy Nash equilibria of this game.
Consider now an altered version of the Bertrand competition environment above in which the (pure)
strategy space of Firm 1 is S₁ = {0,1,2,3,4,5}, the (pure) strategy space of Firm 2 is S2 = {0, 1, 2, 3, 4, 5},
and otherwise the game is the same as the Bertrand competition environment above.
(d) Find the pure-strategy Nash equilibria of this game.
![=
2. Consider a Cournot competition environment with one good and two firms, Firm 1 and Firm 2. The
(pure) strategy space of Firm 1 is S₁ [0, 1], and the strategy s₁ of Firm 1 corresponds to the amount
of the good they produce. Similarly, the (pure) strategy space of Firm 2 is S₂ = [0, 1], and the strategy
82 of Firm 2 corresponds to the amount of the good they produce. If Firm 1 were to produce quantity
8₁ and Firm 2 were to produce quantity 82, the prevailing price in the good market would be 1-81-82,
the utility of Firm 1 would be their profit, u₁ ($1, $2) = (1 - 81 - 82 - c)s1, and the utility of Firm 2
would be their profit, u2($1, $2) = (1-81-82-c)s2, where 0 ≤ c < 1 is the marginal cost of production
for both firms.
(a) Find the pure-strategy Nash equilibria of this game.
(b) Are there other Nash equilibria in this game.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F939ffa75-c788-435b-b74a-4ee3a4182c06%2Fd51afac1-1ef8-4dce-b4e5-545eb08b29f4%2Fgv7eb58_processed.png&w=3840&q=75)
Transcribed Image Text:=
2. Consider a Cournot competition environment with one good and two firms, Firm 1 and Firm 2. The
(pure) strategy space of Firm 1 is S₁ [0, 1], and the strategy s₁ of Firm 1 corresponds to the amount
of the good they produce. Similarly, the (pure) strategy space of Firm 2 is S₂ = [0, 1], and the strategy
82 of Firm 2 corresponds to the amount of the good they produce. If Firm 1 were to produce quantity
8₁ and Firm 2 were to produce quantity 82, the prevailing price in the good market would be 1-81-82,
the utility of Firm 1 would be their profit, u₁ ($1, $2) = (1 - 81 - 82 - c)s1, and the utility of Firm 2
would be their profit, u2($1, $2) = (1-81-82-c)s2, where 0 ≤ c < 1 is the marginal cost of production
for both firms.
(a) Find the pure-strategy Nash equilibria of this game.
(b) Are there other Nash equilibria in this game.
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 2 steps
Recommended textbooks for you
Exploring Economics
Economics
ISBN:
9781544336329
Author:
Robert L. Sexton
Publisher:
SAGE Publications, Inc
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Exploring Economics
Economics
ISBN:
9781544336329
Author:
Robert L. Sexton
Publisher:
SAGE Publications, Inc
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Microeconomics: Principles & Policy
Economics
ISBN:
9781337794992
Author:
William J. Baumol, Alan S. Blinder, John L. Solow
Publisher:
Cengage Learning
Managerial Economics: Applications, Strategies an…
Economics
ISBN:
9781305506381
Author:
James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:
Cengage Learning