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 s2 of Firm 2 corresponds to the amount of the good they produce. If Firm 1 were to produce quantity s₁ and Firm 2 were to produce quantity s2, the prevailing price in the good market would be 1 — 81 — 82, the utility of Firm 1 would be their profit, u₁ (81, 82) = (1-81-82 - c)81, 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.
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 s2 of Firm 2 corresponds to the amount of the good they produce. If Firm 1 were to produce quantity s₁ and Firm 2 were to produce quantity s2, the prevailing price in the good market would be 1 — 81 — 82, the utility of Firm 1 would be their profit, u₁ (81, 82) = (1-81-82 - c)81, 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
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![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
s2 of Firm 2 corresponds to the amount of the good they produce. If Firm 1 were to produce quantity
s₁ and Firm 2 were to produce quantity s2, the prevailing price in the good market would be 1 — 81 — 82,
the utility of Firm 1 would be their profit, u₁ (81, 82) = (1-81-82 - c)81, 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%2F33efa0ee-e3c4-4640-bf2a-d63d72536f00%2F969305b4-cbc0-450f-af06-7872220c1ff1%2Fvwbg5ji_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
s2 of Firm 2 corresponds to the amount of the good they produce. If Firm 1 were to produce quantity
s₁ and Firm 2 were to produce quantity s2, the prevailing price in the good market would be 1 — 81 — 82,
the utility of Firm 1 would be their profit, u₁ (81, 82) = (1-81-82 - c)81, 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.
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