What is the nash cournot equilibrium of the game in which

Question

The n-Firm Cournot Model: Suppose there are n firms in the Cournot oligopoly model. Let qi denote the quantity produced by firm i, and let Q = q_i + ... + q_n denote the aggregate production. Let P(Q) denote the market clearing price (when demand equals Q) and assume that the inverse demand function is given by P(Q) = a - Q, where Q ≤ a. Assume that firms have no fixed cost and that the cost of producing quantity qi is cqi (all firms have the same marginal cost, and assume that c

a. Model this as a normal-form game.

b. What is the Nash (Cournot) equilibrium of the game in which firms choose their quantities simultaneously?

c. What happens to the equilibrium price as n approaches infinity? Is this familiar?