Problem 1 ( Consider a Cournot duopoly with inverse demand funcion 22 - (q +92) if q1 + 92 < 22, if q1 + q2 > 22. P(q1 + 42) 0. The marginal cost of firm 1 is ci = 7, and it is known to all firms while firm 2's marginal cost cz is private information. The probability distribution of however, is known to all firms; c2 can take values of C2, 1 C2 = with probability , 13 with probability . (a) Determine the best response functions of each firm. (b) Derive the set of Bayesian Nash equilibrium of the game.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Problem 1 (
Consider a Cournot duopoly with inverse demand funcion
22 - (q +92) if q1 + 92 < 22,
if q1 + q2 > 22.
P(q1 + 42)
The marginal cost of firm 1 is c = 7, and it is known to all firms while firm
2's marginal cost c2 is private information. The probability distribution of c2,
however, is known to all firms; c2 can take values of
1
C2 =
with probability ,
13 with probability .
(a) Determine the best response functions of each firm.
(b) Derive the set of Bayesian Nash equilibrium of the game.
Transcribed Image Text:Problem 1 ( Consider a Cournot duopoly with inverse demand funcion 22 - (q +92) if q1 + 92 < 22, if q1 + q2 > 22. P(q1 + 42) The marginal cost of firm 1 is c = 7, and it is known to all firms while firm 2's marginal cost c2 is private information. The probability distribution of c2, however, is known to all firms; c2 can take values of 1 C2 = with probability , 13 with probability . (a) Determine the best response functions of each firm. (b) Derive the set of Bayesian Nash equilibrium of the game.
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