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10. Consider the Cournot duopoly game with incomplete information. First, nature chooses a number x, which is equally likely to be 8 or 4. This number represents whether demand is high (x = 8) or low (x = 4). Firm 1 observes x because this firm has performed market research and knows the demand curve. Firm 2 does not observe x. Then the two firms simultaneously select quantities, q1 and 92, and the market price is determined by p = x - 91 - 92. Assume that the firms produce at zero cost. Thus, the payoff of firm 1 is (x - 91 - 92)91, and the payoff of firm 2 is (x - 91 - 92)92. (a) Note that there are two types of firm 1, the high type (observing x = 8) and the low type (observing x = 4). Let qr and q7 denote the quantity choices of the high and low types of firm 1. Calculate the players' best- response functions. () Find the Bayesian Nash equilibrium of this game. (c) Does firm I's information give it an advantage over firm 2 in this game? Quantify this