What is Bertrand competition in simple terms?

Firms selling the same product compete on price. Since pricing just a bit lower wins all the customers, they keep undercutting each other.

What is the Bertrand paradox?

It's the theoretical result that even with only two firms, price falls to cost and profits hit zero. In real markets, capacity limits, product differences and repeated dealings usually keep prices from falling that far.

Bertrand Competition

📈 Economics By CampusDown Wiki Editorial Team Last updated October 27, 2026

Bertrand competition is an oligopoly model put forward in 1883 by the French mathematician Joseph Bertrand as a critique of Cournot's model. Firms selling a homogeneous product compete by setting prices simultaneously rather than quantities. Since undercutting a rival even slightly captures the whole market, the key result is the Bertrand paradox: with just two firms, price falls to marginal cost.

Contents

1. Bertrand's critique and the paradox
2. Resolving the paradox
3. Price dispersion and experimental evidence
4. FAQ
5. References

Bertrand's critique and the paradox

Reviewing Cournot's (1838) book, Bertrand (1883) pointed out that what firms actually choose is price, not quantity. If two firms producing a homogeneous good at the same marginal cost set prices, either can capture every customer by pricing just below the other, so there is a constant incentive to undercut. The unique Nash equilibrium is for both firms to price at marginal cost and earn zero profit. Because this conclusion, that two firms suffice for the perfectly competitive outcome, clashes with the profits observed in real oligopolies, it is called the Bertrand paradox.

Resolving the paradox

Edgeworth (1897) showed that if firms have limited capacity, cutting price does not let them serve all demand, so prices need not fall to marginal cost and may instead cycle. Kreps and Scheinkman (1983) proved that if firms first choose capacity and then compete on price, the outcome coincides with the Cournot equilibrium. Hotelling (1929) showed that product differentiation, in which consumers value firms differently by location or taste, keeps prices above marginal cost, and Singh and Vives (1984) showed that in a differentiated duopoly price competition is more competitive than quantity competition. Friedman's (1971) analysis of repeated games showed that when interaction repeats indefinitely, collusive prices can be sustained.

Price dispersion and experimental evidence

Varian (1980) explained that when only some consumers compare prices, firms randomize their discounts in a mixed-strategy equilibrium, producing price dispersion for identical goods. Baye, Morgan and Scholten (2004) presented evidence that substantial price dispersion persists even on an internet price comparison site, and Baye and Morgan (1999) showed that under demand conditions allowing unbounded profits, equilibria with positive profits can exist even in one-shot Bertrand games. In experiments by Dufwenberg and Gneezy (2000), prices in two-firm markets stayed above marginal cost, but with three or four firms they quickly converged toward it. Tirole (1988) and Vives (1999) established the Bertrand model as a basic framework of industrial organization.

FAQ

What is Bertrand competition in simple terms?: Firms selling the same product compete on price. Since pricing just a bit lower wins all the customers, they keep undercutting each other.
What is the Bertrand paradox?: It's the theoretical result that even with only two firms, price falls to cost and profits hit zero. In real markets, capacity limits, product differences and repeated dealings usually keep prices from falling that far.

Sources reviewed: 2026-10-26

References

Bertrand, J. (1883). Review of Walras's Théorie mathématique de la richesse sociale and Cournot's Recherches. Journal des Savants, 67, 499–508.
Cournot, A. A. (1838). Recherches sur les principes mathématiques de la théorie des richesses. Paris: Hachette.
Edgeworth, F. Y. (1897). La teoria pura del monopolio. Giornale degli Economisti, 15, 13–31.
Hotelling, H. (1929). Stability in competition. Economic Journal, 39(153), 41–57.
Kreps, D. M., & Scheinkman, J. A. (1983). Quantity precommitment and Bertrand competition yield Cournot outcomes. Bell Journal of Economics, 14(2), 326–337.
Singh, N., & Vives, X. (1984). Price and quantity competition in a differentiated duopoly. RAND Journal of Economics, 15(4), 546–554.
Tirole, J. (1988). The Theory of Industrial Organization. Cambridge, MA: MIT Press.
Friedman, J. W. (1971). A non-cooperative equilibrium for supergames. Review of Economic Studies, 38(1), 1–12.
Baye, M. R., & Morgan, J. (1999). A folk theorem for one-shot Bertrand games. Economics Letters, 65(1), 59–65.
Dufwenberg, M., & Gneezy, U. (2000). Price competition and market concentration: An experimental study. International Journal of Industrial Organization, 18(1), 7–22.
Varian, H. R. (1980). A model of sales. American Economic Review, 70(4), 651–659.
Baye, M. R., Morgan, J., & Scholten, P. (2004). Price dispersion in the small and in the large: Evidence from an internet price comparison site. Journal of Industrial Economics, 52(4), 463–496.
Vives, X. (1999). Oligopoly Pricing: Old Ideas and New Tools. Cambridge, MA: MIT Press.

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This article was last updated on October 27, 2026. It is based on widely recognized original works and textbooks; when citing it in a paper, please check the original sources listed in the references.