Duopoly
A duopoly is a market structure in which two firms supply the entire market or dominate it. It is a special case of oligopoly, in which a small number of firms account for most output. Duopolies are of particular interest because the strategic interaction between just two rivals is tractable to model and yet captures the essential features of competition under interdependence. Classic models of duopoly, including those of Cournot and Bertrand, illustrate how the number and behaviour of firms affect prices, output, and welfare.
Characteristics
A duopoly is characterised by high concentration, interdependence of decisions, and barriers to entry. Each firm's profit depends not only on its own actions but also on the actions of its rival, so each must anticipate the other's response. Barriers to entry, whether technological, regulatory, or created by the incumbents, allow the two firms to earn above-normal profits without attracting new competitors. The product may be homogeneous or differentiated, which affects the intensity of price competition.
Classic models
In the Cournot model, each firm chooses the quantity to produce, taking the rival's quantity as given. The resulting equilibrium, known as the Cournot-Nash equilibrium, yields output between the monopoly and competitive levels and prices above marginal cost. With two identical firms and linear demand and cost, each produces one-third of the competitive output and the price is two-thirds of the way from marginal cost to the monopoly price.
In the Bertrand model, each firm chooses price, taking the rival's price as given. With homogeneous products and identical costs, the equilibrium drives price to marginal cost, replicating the competitive outcome despite the presence of only two firms. This result, known as the Bertrand paradox, is resolved when products are differentiated, capacities are constrained, or the game is repeated.
Stackelberg competition models sequential decision-making, in which a leader commits to an output or price and the follower responds. The leader typically earns higher profit, illustrating the value of moving first.
Price and non-price competition
Duopolists may compete on price, quantity, quality, advertising, or product features. They may also collude, explicitly or tacitly, to raise prices toward monopoly levels. Collusion is easier to sustain when firms interact repeatedly, discount rates are low, and cheating can be detected and punished. In many jurisdictions, explicit price-fixing is illegal, and authorities scrutinise mergers that would create or strengthen duopolies.
Repeated interaction can support cooperative outcomes through strategies such as tit-for-tat, in which each firm matches the rival's previous action. However, the temptation to undercut always exists, and coordination can break down, leading to price wars.
Examples and welfare
Real-world duopolies appear in aviation, soft drinks, commercial aircraft, credit cards, and some digital markets, where network effects and scale economies limit the number of viable competitors. Regulators examine such markets closely because duopolies can produce prices well above competitive levels and can dampen innovation, though they can also compete vigorously on quality and cost.
Welfare analysis compares duopoly outcomes with the competitive benchmark. Cournot duopoly produces less output and higher prices than perfect competition, generating a deadweight loss. Horizontal mergers that reduce the number of firms from three to two can raise prices appreciably, which is why competition authorities often scrutinise them.
Duopoly and game theory
The analysis of duopoly is a cornerstone of game theory and industrial organisation. Because each firm's payoff depends on the other's choice, the equilibrium concept of Nash, in which neither firm can improve its payoff by changing its own strategy given the other's, is the natural solution. Cournot and Bertrand equilibria are Nash equilibria of quantity and price games respectively.
Repeated games show how cooperation can emerge. In an infinitely repeated duopoly, trigger strategies can sustain collusion as an equilibrium, provided firms value future profits sufficiently and can detect and punish deviations. The Folk Theorem establishes that a wide range of outcomes can be sustained in repeated games, which explains why collusion is possible but not guaranteed.
Entry, deterrence and regulation
Duopolists may act to deter entry by setting low prices, investing in capacity, or building brand loyalty. Limit pricing, in which an incumbent sets a price low enough to make entry unprofitable, is a classic deterrence strategy. Advertising and product proliferation can raise the cost of entry and entrench incumbents. Such conduct is scrutinised under competition law when it amounts to abuse of dominance.
Merger policy pays particular attention to markets with few competitors, because reducing the number of firms from three to two can raise prices appreciably. Remedies such as divestitures, behavioural commitments, and access obligations are used to preserve competition when mergers are permitted.
Empirical evidence
Empirical studies of duopolies and concentrated markets find that prices are typically above competitive levels, though the extent varies with product differentiation, capacity constraints, and the intensity of competition. Studies of airline routes, for example, find that routes served by fewer airlines have higher fares. Studies of digital markets find that network effects and data advantages can entrench leading firms, raising barriers to entry and limiting the disciplining effect of potential competition.