Reference no: EM132422766

Consider Firm 1 and Firm 2, who produce identical products and compete in a market with the inverse demand curve p(y) = 20-y. Their competition goes on for infinitely many periods. In each period they simultaneously choose their quantities, and produce at zero cost. They discount future profits using a discount factor δ < 1.

The firms would like to collude so each can obtain half of the monopoly profits. For what discount factors, can they play a Subgame Perfect Nash Equilibrium in which they obtain this desired outcome in every period? Be clear about what strategy profile you propose, and show that if the discount factor is high enough, then there is no profitable deviation for either firm at any possible subgame.