Suppose we have a Cournot duopoly game with some incomplete information. Market demand is P= 15 - Q, where Q is the sum of Q1 and Q2. Firm 1's total cost is 3*Q1. Firm 2's cost is private information. With probability , it is 4*Q2 and with probability it is 2*Q2. Find the Bayesian Nash equilibrium of this game. You will need to find three Best response functions: one for the low-cost Firm 2, one for the High-cost Firm 2 and one for Firm 1. Each of the types of Firm 2 must be best-responding to Firm 1 in equilibrium , while Firm 1 will be best-responding to both types of firm 2 with the appropriate probabilities. (Firm 1's profit function will be times its profit if facing the low-cost form 2 plus its profit if facing the high-cost type.) Compare your results to the outcome of the two complete information games: one where firm 2 has unit cost of 4 and the other where it has unit cost of 2.