Cournot Duopoly
Two firms choose quantities simultaneously — reaction functions, Nash equilibrium, and efficiency benchmarks
Cournot competition (1838): each firm maximizes profit given the other's output, leading to a Nash equilibrium where neither can unilaterally improve. With inverse demand P = a − b(q₁+q₂) and marginal costs c₁, c₂:
Reaction functions: q₁* = (a − c₁ − b·q₂) / (2b), q₂* = (a − c₂ − b·q₁) / (2b)
Nash equilibrium: q₁ᴺ = (a − 2c₁ + c₂) / (3b), q₂ᴺ = (a − 2c₂ + c₁) / (3b)
The Cournot outcome lies between monopoly (collusive, maximizes joint profit) and perfect competition (P = MC). With N firms, price converges to competitive as N→∞.