Cournot Competition

A simultaneous-move duopoly/oligopoly with quantity as the strategic variable.

Ask the Game theory assistant1 min read · Updated September 9, 2026

Definition

Firms simultaneously choose quantities $q_i\ge 0$ and receive profit $\pi_i=q_i P(Q)-c_i(q_i)$ where $Q=\sum_j q_j$ .

The Cournot-Nash equilibrium solves $\partial\pi_i/\partial q_i=0$ for all $i$ simultaneously.

Intuition

Each firm takes rivals' output as given and equates marginal revenue to marginal cost.

Equilibrium lies between monopoly and perfect competition.

Worked example

With linear demand $P=a-Q$ and zero cost, symmetric equilibrium is $q_i^*=a/(n+1)$ and price $P=a/(n+1)$ ; as $n\to\infty$ , $P\to 0$ .

Two firms with these parameters earn $\pi=a^2/9$ each.

The math

Best response $q_i^*(q_{-i})=\tfrac{1}{2}(a-\sum_{j\ne i}q_j)$ in the linear case; intersection gives the Nash equilibrium.

As $n\to\infty$ , the Cournot equilibrium converges to the competitive outcome (Walras).

Where it is used

The OPEC oil cartel's production decisions approximate Cournot competition among member nations. Each country chooses its output quantity knowing that aggregate supply affects the world oil price, and the model predicts how production quotas affect prices.

In the global semiconductor industry, major manufacturers like TSMC, Samsung, and Intel engage in quantity competition: each decides fab capacity independently, and the total installed capacity determines chip prices in downstream markets worldwide.

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