Problem B [5 points] Consider a Cournot duopoly operating in a market with inverse demand P(Q)= a - Q, where Q = q1 + q2 is the aggregate quantity on the market. . Both firms have total costs Ci(q;) = cq;, for i = 1, 2, but demand is uncertain: it is high ( a = aw ) with probability p and low ( a = a_) with probability 1 - p. Firm 1 knows whether demand is high or low, but firm 2 does not. . All of this is common knowledge. . The two firms simultaneously choose quantities. 1. Describe the situation as a Bayesian game (players, action spaces, type spaces, beliefs, and utility functions). [1 point] 2. Assume that the parameters of the model are chosen such that all equilibrium quantities are positive. a. What is the Bayesian equilibrium of this game? [2 points] b. Does having superior information beneficial in this Bayesian game? Explain clearly as possible. [1 point] 3. When does this situation correspond to Cournot duopoly with perfect information? [1 point]