This is question regarding GAME THEORY! ?

Question

1. Consider a Cournot duopoly operating in a market with inverse demand P(Q) =

a ¡ Q, where Q = q1 + q2 is the aggregate quantity on the market. Both ¯rms

have total costs ci(qi) = cqi, but demand is uncertain: it is high (a = aH) with

probability µ and low (a = aL) with probability 1 ¡ µ. Furthermore, information

is asymmetric: ¯rm 1 knows whether demand is high or low, but ¯rm 2 does not.

All of this is common knowledge. The two ¯rms simultaneously choose quantities.

What are the strategy spaces for the two ¯rms? What is the Bayesian Nash

equilibrium of this game, (assuming aH; aL; µ and c are such that all equilibrium

quantities are positive)?

Answer 1

i)

q² = (θqh + (1-θ)al - c)) / 3

q¹h = ((3-θ)ah - (3-θ)al - 2c)) / 6

q¹l = ((2+θ)al - (3-θ)ah - 2c)) / 6

ii)

(2+θ)al - θah - 2c >0

It's question #3 here: http://iclass.shufe.edu.cn/teacherweb/us...

Problem set 3: http://iclass.shufe.edu.cn/teacherweb/us...

Answer 2

John Nash is brilliant.