Cournot's duopoly game with imperfect information: -
Consider the game when the inverse demand function is given by P(Q) = α - Q for Q ≤ α and P(Q) = 0 for Q > α. For values of cH and cL close enough that there is a Nash equilibrium in which all outputs are positive, find this equilibrium.
Compare this equilibrium with the Nash equilibrium of the game in which firm 1 knows that firm 2's unit cost is cL, and with the Nash equilibrium of the game in which firm 1 knows that firm 2's unit cost is cH.