Cournot Competition

Also known as · Cournot duopoly · quantity competition

Cournot competition is the simultaneous quantity-setting model of oligopoly: firms choose $q_i$ independently, the market price clears at $P(q_1 + q_2)$ , and the equilibrium is the Nash Equilibrium where each firm's reaction function (best response in quantities) crosses the other's. For the symmetric duopoly with $P = A - Q$ and $C_i = c q_i$ :

q_1^* = q_2^* = \frac{A-c}{3}, \quad P^* = \frac{A+2c}{3}, \quad \Pi_i = \left(\frac{A-c}{3}\right)^2.

Industry output is higher and price is lower than monopoly but higher / lower than perfect competition — Cournot sits between the two.

type: reaction-functions
br1: 4.5,-0.5
br2: 4.5,-0.5

When to use

Cournot is the right model when firms commit to capacity or production levels in advance and price clears the market afterwards (commodities, electricity, agriculture). Quantities are strategic substitutes — both best-response functions slope down. Comparative-statics: more firms → industry output rises, price falls, per-firm profit shrinks, and in the limit $N \to \infty$ Cournot converges to perfect competition.

Cournot Competition

When to use

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