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Consider a Cournot duopoly model where the market price is given by the inverse demand function: p= 30 - 3.91 - 92. And suppose each firm produces at a cost of 25 per unit of production (ie, total costs are given by 25. q: for i = 1,2). (a) Find the payoff functions uz (91, 92) and uz (91, 92). (b) Suppose player 1 believes that player 2 is equally likely to produce q2 = 10, 92 = 15, 92 18 and 92 22 units, and these are the only production values player 1 believes player 2 can choose. Let 82 denote these beliefs for player 1. Compute u. (01,02) for these beliefs 02. (c) Suppose player 2 believes that player 1 will produce qı = 13 with probability 1/3, 91 10 with probability 1/4, and qı 16 with probability 5/12, and these are the only production values player 2 believes player 1 can choose. Let @ denote these beliefs for player 2. Compute uz (@1, 92) for these beliefs 01.
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