Problem 3: Consider the following Stackelberg duopoly with incomplete information. Suppose that the marginal cost of firm 1 (F1) c1 is uniformly distributed over [0,1] and the marginal cost of firm 2 (F2) C2 is uniformly distributed over [0,1]. Let P (Q) = a-Q if Qsa and P(Q) = 0 if Q> a. We assume that all quantities are positive. Nature chooses the cost c1 of firm 1 and the cost c2 of firm 2. Firm 1 observes c1 (but firm 1 does not observe c2) and chooses its quantity q1 2 0. Firm 2 observes c2 and q1 and chooses its quantity q2 2 0. Profits are received Describe the sets of types and strategies of each firm. Calculate the PBE of this dynamic game (in the PBE, you don't need to specify any beliefs). Determine the condition necessary for all the quantities found for firm 1 to be non-negative. Also determine the necessary condition so that all the quantities found in firm 2 are non-negative. Problem 3: Consider the following Stackelberg duopoly with incomplete information. Suppose that the marginal cost of firm 1 (F1) c1 is uniformly distributed over [0,1] and the marginal cost of firm 2 (F2) C2 is uniformly distributed over [0,1]. Let P (Q) = a-Q if Qsa and P(Q) = 0 if Q> a. We assume that all quantities are positive. Nature chooses the cost c1 of firm 1 and the cost c2 of firm 2. Firm 1 observes c1 (but firm 1 does not observe c2) and chooses its quantity q1 2 0. Firm 2 observes c2 and q1 and chooses its quantity q2 2 0. Profits are received Describe the sets of types and strategies of each firm. Calculate the PBE of this dynamic game (in the PBE, you don't need to specify any beliefs). Determine the condition necessary for all the quantities found for firm 1 to be non-negative. Also determine the necessary condition so that all the quantities found in firm 2 are non-negative