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, but demand is
uncertain: it is High (a = aH) with probability theta and low (a=
aL) with probability 1 - theta. Furthermore, information is
asymmetric: firm 1 knows whether demand is high or low, but firm 2
does not. All this is common knowledge. What are the stategy spaces
for the two firms? What is the Bayesian Nash Equilibrium of this
game?