Question

Problem 2. Gibbons 1.5 Consider the following two finite versions of the Cournot duopoly model. First, suppose each firm must choose either half the monopoly quantity, 4m/2 = (a - c)/4, or the Cournot equilibrium quantity, 4c = (a - c)/3. No other quantities are feasible. Show that this two-action game is equivalent to the Prisoner's Dilemma: each firm has a strictly dominated strategy, and both are worse off in equilibrium than they would be if they cooperated. Second, suppose each firm can choose either (m/2, or qc, or a third quantity, q'. Find a value for q' such that the game is equivalent to the Cournot model, in the sense that (qc, qc) is a unique Nash equilibrium and both firms are worse off in equilibrium than they would be if they cooperated, but neither firm has a strictly dominated strategy.

Answer 1

solution:- If in case of both fromg generate half of the quantity of monopoly (1.99 by each of them. Hence Qe Qm = Queries If both fioms comhete, Quantity prodreced by either from Q = -= Qc: [couronot couilibrium quantity). * Two action game :- Here M=monopay. c=cournot. I E U

→ Here each and every from hous au strictly dominant Strategy given by Ic=0C, producing cannot caulibrium Quantity. > This is equivalent to poisoner's dilemma, why because, Producing of monopoly ouantities givers total profit of Casch from which is far greater than (c)2 are generated by eauch from in cournot equilibrium market. > Honce, it's not a optimal strategy as it is strictly dominated by producing covonot Quantity.