Game Theory

Cournot (quantity) and Stackelberg (sequential)

Two identical firms, Firm 1 and Firm 2, compete in quantity in a market where inverse demand is P(Q) = 100 − Q and there exists a constant marginal cost of 20 per unit.

(a) Find the Cournot equilibrium

i. Find the response functions q1(q2) and q2(q1)

ii. Plot the response functions on a single graph with the axes labeled

iii. Find the quantities ˆ q1 and ˆ q2 corresponding to the intersection of the response functions

(b) Find the Stackelberg equilibrium

i. If Firm 1 moves first, what is the profit maximizing level of production, q1*?

ii. Find Firm 2’s level of production, q2*, given what you found in part i.