ourvle.mona.uwi.edu 18. Imperfect information: informati... )) |5 Exercise 611 Question 15 e Another... faculty.ses.wsu.edu/Espinola/Homewo. qed.econ.queensu.ca/pub/students/k. (1,189 unrea 4. Consider the Cournot duopoly game where Firm I, and Firm II are two quantity - setting firms competing in an industry as duopolists. The demand function for the market is given by P = M - q1 - 92, where M is a constant and the marginal cost is constant at c. (a) Suppose the Cournot - Nash equilibrium occurs at the point (q1, q2). Prove that (i) 91 - 92 = = ( M - C), [10] (ii) the equilibrium profits for each firm is 3 (M - c) ]2. [5] (b) In the Cournot duopoly game presented above it is common knowledge that both firms have marginal cost c. Suppose this continues to be true for Firm II's marginal cost, but that Firm I's marginal cost is now known only by Firm I, so that Firm II is forced to guess at it when it makes its production decision. Take it to be common knowledge that Firm II is sure that Firm I's marginal cost is in the set C = {C1, C2, C3) and attaches a probability ri to each alternative ci for i = 1,2,3. Both firms want to maximize expected profit. Model this situation by introducing an initial move by Nature that selects Firm I's marginal cost. Firm I learns of the outcome of Nature's move, but Firm II does not. Then the Cournot game is played. (i) Draw the strategic form for this situation. You do not need to include the payoffs. (ii) [5] Explain why a pure strategy q2 for Firm II is just a number in the MacBook Air 80 F4 FO DII F8 DD F9 @ FF $ 2 W 4 5 6 O W E R T Y U O P S D F G H K X C V B N M <