Microeconomics: Cournot

Suppose there are n symmetric firms in a Cournot oligopoly. Inverse demand is given by P(Q)=aQ where Q=i=1nqi. The firms are symmetric with no fixed cost and a constant marginal cost that is equal to c(0,a). Consider the infinitely repeated game based on this stage game in which the firms discount the future using a discount factor (0,1) and pursue the objective of maximizing the present discounted value of their own payoffs. Derive the lowest value of such that the firms can use grim trigger strategies (that switch forever to the stagegame Nash equilibrium after any deviation) to sustain the monopoly price level in a subgameperfect Nash equilibrium. How does this critical level of the discount factor depend on the number of firms, n ? Explain the economic intuition of your answer. Suppose there are n symmetric firms in a Cournot oligopoly. Inverse demand is given by P(Q)=aQ where Q=i=1nqi. The firms are symmetric with no fixed cost and a constant marginal cost that is equal to c(0,a). Consider the infinitely repeated game based on this stage game in which the firms discount the future using a discount factor (0,1) and pursue the objective of maximizing the present discounted value of their own payoffs. Derive the lowest value of such that the firms can use grim trigger strategies (that switch forever to the stagegame Nash equilibrium after any deviation) to sustain the monopoly price level in a subgameperfect Nash equilibrium. How does this critical level of the discount factor depend on the number of firms, n ? Explain the economic intuition of your