Game Theory: Equilibrium in Dynamic Games Three monopoly firms manipulate a market with a given inverse demand curve P(Q
Posted: Sun May 29, 2022 6:55 pm
Game Theory: Equilibrium in Dynamic Games
Three monopoly firms manipulate a market with a given inverse
demand curve P(Q) = a - Q, where Q = q1 + q2 + q3, and qi
represents firm i's output. The marginal cost of each firm is fixed
at c, and there are no fixed costs. Firms dynamically choose their
output as follows: Firm 1, the leader in the industry, chooses q1.
After that, Firm 2 and Firm 3 will observe q1 and
then choose q2 and q3 respectively at the same time.
a. How many possible subgames does this dynamic game have?
Briefly explain why.
b. Is the game a perfect information game or an imperfect
information game? Briefly explain why.
c. What is the subgame perfect equilibrium of this game? prove its
uniqueness.
d. Find a Nash equilibrium that is not a subgame perfect
equilibrium.
Three monopoly firms manipulate a market with a given inverse
demand curve P(Q) = a - Q, where Q = q1 + q2 + q3, and qi
represents firm i's output. The marginal cost of each firm is fixed
at c, and there are no fixed costs. Firms dynamically choose their
output as follows: Firm 1, the leader in the industry, chooses q1.
After that, Firm 2 and Firm 3 will observe q1 and
then choose q2 and q3 respectively at the same time.
a. How many possible subgames does this dynamic game have?
Briefly explain why.
b. Is the game a perfect information game or an imperfect
information game? Briefly explain why.
c. What is the subgame perfect equilibrium of this game? prove its
uniqueness.
d. Find a Nash equilibrium that is not a subgame perfect
equilibrium.