(Don't copy the answe)r 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.