Cournot Competition
What is Cournot Competition?
Cournot competition is an oligopoly model where firms simultaneously choose how much quantity to produce, and the combined output sets the market price.
Each firm picks its output taking rivals' outputs as given, and equilibrium occurs where their reaction functions intersect (a Nash equilibrium in quantities). The result lies between monopoly and perfect competition: price exceeds marginal cost and firms earn positive profit, but less than a monopolist would. As the number of firms rises, the outcome approaches the competitive one.
Cournot Competition: a worked example
Two firms face P = 100 - Q with marginal cost of $10 each. Firm 1's profit is (90 - q1 - q2)q1, so its reaction function is q1 = 45 - q2/2, and firm 2's mirrors it. Setting q = 45 - q/2 gives q = 30 for each firm. Total output is 60, price is $40, and each earns ($40 - $10) x 30 = $900. Set that against the extremes: a monopolist would produce 45 units, and a perfectly competitive industry would produce 90, where price equals the $10 cost. Cournot's 60 sits between them, which is the whole point of the model.
The mistake students make with cournot competition
The usual slip is taking marginal revenue off the market demand curve. Students write MR = 100 - 2Q, set it equal to $10, get Q = 45 and split it 22.5 apiece. That is the collusive outcome, not Cournot. Each firm's marginal revenue comes from its residual demand with the rival's output held fixed, so firm 1 faces MR = 100 - 2q1 - q2. The shortcut appeals because it recycles the monopoly rule, but it forgets that firm 1 captures only its own extra sales while the price drop hits both firms.
Cournot Competition questions
What is a cournot reaction function?
A Cournot reaction function gives one firm's profit-maximizing output for every quantity the rival might choose. You derive it by maximizing that firm's profit while treating the rival's quantity as a constant. It slopes downward, because more output from a rival lowers price and makes producing less attractive. Cournot equilibrium sits where both reaction functions cross, so each firm is best-responding to what the other actually does.
What happens to cournot equilibrium as more firms enter?
Cournot equilibrium converges toward the perfectly competitive outcome as firms are added. With n identical firms facing demand P = a - bQ and marginal cost c, each firm produces (a - c) divided by ((n + 1)b), and price works out to (a + nc)/(n + 1). One firm gives the monopoly result; as n grows large, price approaches marginal cost and per-firm profit approaches zero.
Is cournot competition a nash equilibrium?
Cournot competition is solved as a Nash equilibrium in quantities. Each firm's output is a best response to the rival's actual output, so no firm can raise its profit by unilaterally producing more or less. The Cournot outcome is not the joint-profit maximum, though. Both firms would earn more by agreeing to restrict output, but that agreement is not a Nash equilibrium, because each firm gains by quietly exceeding its quota.
Formula / Example
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