Consider the Cournot duopoly. Suppose that the demand curve is now(q1+q2) = 1302(q1+q2). Suppose that firms 1 and 2 simultaneously choose quantityq1andq2to supply and that the firms incur a marginal cost of production equal to 10. Assume that the quantities that each firm can supply are[0,65].As a result, each firm's utility function is given by:

u1(q1, q2) = (1302(q1+q2))q110q1

u2(q1, q2) = (1302(q1+q2))q210q2.

Part a: If firm 2 produces quantityq2, what is the best response for firm 1? Use this to solve for the best response function for firm 1, BR1(q2). Similarly solve for the best response function for firm 2, BR2(q2).

Part b: What are the strictly dominated strategies of each firm in this game? Justify why each of these strategies is strictly dominated. Justify why all other strategies are not strictly dominated.

Part c: After having eliminated the strictly dominated strategies found in part a, what are the strictly dominated strategies in the reduced game? Provide justification again.

Part d: What are the rationalizable strategies for each player? What are the rationalizable strategy profiles?