Find the Bayesian Nash Equilibrium. Briefly explain the intuition behind each of the steps you are taking to get the answer.

Cournot Duopoly with Incomplete Information:

Let us consider a Cournot oligopoly game where two firms compete in quantities. While both firms have the same marginal costs, MC = 2, they are asymmetrically informed about the actual state of the market demand.
In particular, firm 2 does not know what the actual state of the market demand is, but know that it is distributed with the following probability distribution:

P(Q) = 20 – Q with probability 2/3
P(Q) = 8 – Q with probability 1/3

Firm 1 know the actual state of the market demand, and firm 2 knows that firm 1 has this information.

Find the Bayesian Nash Equilibrium. Briefly explain the intuition behind each of the steps you are taking to get the answer. (15 marks)