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
firms have total costs ci(qi)=cqi (notice that i is a small subscript
to c and q), but demand is uncertain: it is high (a=aH) with
probability theta and low (a=aH) with probability 1-theta.
Furthermore, information is asymmetric: firm 1 knows whether demand is
high or low, but firm 2 does not. All of this is common knowledge. The
two firms simultaneously choose quantities. What are the strategy
spaces for the two firms? Make assumptions concerning aH, aL, theta,
and c such that all equilibrium quantities are positive. What is the
Bayesian Nash equilibrium of this game? (notice that H and L are both
small subscript to a as well) |
