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

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?

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