Question

Consider the Cournot duopoly model in which two firms, 1 and 2, simultaneously choose the quantities they supply, q1 and q2. The price each will face is determined by the market demand function p(q1 , q2 ) = 3 − 1/4 (q1 + q2 ). Each firm has a probability 1/2 of having a marginal unit cost of cL = 1 and a probability 1/2 of having a marginal unit cost of cH = 2. These probabilities are common knowledge, but the true type is revealed only to each firm individually. Solve for the Bayesian Nash equilibrium.

Answer 1

Bayesian Nash equilibrium in the Cournot duopoly model is achieved when both firms choose the quantities that maximize their expected profits, given the probability distribution of their costs.

Step-by-step explanation:

Bayesian Nash equilibrium in the Cournot duopoly model is achieved when both firms choose the quantities that maximize their expected profits, given the probability distribution of their costs. In this case, Firm 1 and Firm 2 have a 50% chance to have a marginal unit cost of 1, and a 50% chance to have a marginal unit cost of 2. Given this information, the firms will consider their expected profits for each possible combination of quantities, taking into account the market demand function, and choose the quantity that maximizes their expected profit.