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Three oligopolists operate in a market with inverse demand given by p (Q ) = a...

Three oligopolists operate in a market with inverse demand given by p (Q ) = a −Q , where Q = q1 + q2 + q3, and qi is the quantity produced by firm i. Each firm has a constant marginal cost of production, c and no fixed cost. The firms choose their quantities dy- namically as follows: (1) Firm 1, who is the industry leader, chooses q1 ≥ 0; (2) Firms 2 and 3 observe q1 and then simultaneously choose q2 and q3 respectively.

(A) How many proper subgames does this dynamic game have? Explain Briefly.

(B) Is it a game of perfect or imperfect information? Explain Briefly.

(C) What is the Subgame-Perfect Equilibrium of this game? Show that it is unique.

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Answer #1

(A) It is a Stackelberg game and within it we have Cournot game between firm 2 and firm 3 as they both are follower firms and decide output simultaneously .

So there is one proper subgame which is Cournot game in this dynamic game.

(B) It is a game of perfect information because each firm is aware of moves of other firm.

In this we find the equilibrium quantity of leader them as it decides it first and then accordingly the followers choose their equilibrium quantities.

(C)

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