02 Jun Question Consider a Cournot duopoly model where the market
Question
Consider a Cournot duopoly model where the market price is given by the inverse demand function:
p = 30 ? 3 ? q1 ? q2.
And suppose each firm produces at a cost of 25 per unit of production (i.e, total costs are given by 25 ? qi
for i = 1, 2).
(a) Find the payoff functions u1 (q1, q2) and u2 (q1, q2).
(b) Suppose player 1 believes that player 2 is equally likely to produce q2 = 10, q2 = 15, q2 = 18 and q2 = 22 units, and these are the only production values player 1 believes player 2 can choose. Let ?2 denote these beliefs for player 1.
Compute u1 (q1, ?2) for these beliefs ?2.
(c) Suppose player 2 believes that player 1 will produce q1 = 13 with probability 1/3,
q1 = 10 with probability 1/4, and q1 = 16 with probability 5/12, and these are the only production values player 2 believes player 1 can choose. Let ?1 denote these beliefs for player 2. Compute u2 (?1, q2) for these beliefs ?1.
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