Consider the following duopoly where firms choose their quantities (qi ∈ [0, ∞)) simultaneously. Firm 1 has a cost of c1 (q1) = 20q1 and firm 2 knows this cost. Firm 2 has either a cost of c2 H (q2) = 30q2 or a low cost of c2 L (q2) = 15q2. Firm 2 knows their cost, but firm 1 doesn’t know firm 2’s cost, but believes that firm 2 has a high cost with probability 1/3 and a low cost with probability 2/3. The market demand curve is...
P(Q) = ( 120 − 4Q Q < 30 ) 0 otherwise
a) Find the Nash equilibrium of the Bayesian game.
b) Determine the profits in equilibrium.