Consider the following modified Cournot-game. Firm 2 is run by its owner whereas Firm 1 is run by a manager whose preferences are represented by the following payoff function u(91, 92) = II₁ (91, 92) + aq₁ and the marked demand function is P = 1 - Q. The game is played as follows. In the first stage the owner of the Firm 1 chooses 0 < a < 1. Then the manager of Firm 1 and the owner of Firm 2 observes a and choose q₁ and q2 to maximize u and II₂ respectively. What are the subgame-perfect equilibrium levels of a, q₁ and 92?
Consider the following modified Cournot-game. Firm 2 is run by its owner whereas Firm 1 is run by a manager whose preferences are represented by the following payoff function u(91, 92) = II₁ (91, 92) + aq₁ and the marked demand function is P = 1 - Q. The game is played as follows. In the first stage the owner of the Firm 1 chooses 0 < a < 1. Then the manager of Firm 1 and the owner of Firm 2 observes a and choose q₁ and q2 to maximize u and II₂ respectively. What are the subgame-perfect equilibrium levels of a, q₁ and 92?
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.1P
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![Consider the following modified Cournot-game. Firm 2 is run by its owner whereas Firm 1 is run by a
manager whose preferences are represented by the following payoff function u(9₁, 92) = II1₁ (91, 92) + aqı
and the marked demand function is P = 1 – Q. The game is played as follows. In the first stage the
owner of the Firm 1 chooses 0 < a < 1. Then the manager of Firm 1 and the owner of Firm 2 observes
a and choose 9₁ and 92 to maximize u and II₂ respectively. What are the subgame-perfect equilibrium
levels of a, 9₁ and 92?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff92bbc9-4771-4f73-9c94-32866f8889ad%2F7c6180ce-57ba-4e54-bb3f-88c5eac111ec%2Flchflio_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following modified Cournot-game. Firm 2 is run by its owner whereas Firm 1 is run by a
manager whose preferences are represented by the following payoff function u(9₁, 92) = II1₁ (91, 92) + aqı
and the marked demand function is P = 1 – Q. The game is played as follows. In the first stage the
owner of the Firm 1 chooses 0 < a < 1. Then the manager of Firm 1 and the owner of Firm 2 observes
a and choose 9₁ and 92 to maximize u and II₂ respectively. What are the subgame-perfect equilibrium
levels of a, 9₁ and 92?
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