The Bertrand and Cournot models are the two basic and fundamental economic models aimed at capturing strategic interaction between a limited number of firms active in a particular market (i.e. oligopoly competition). Where the Bertrand model (Bertrand, 1883) assumes that firms compete on price and subsequently produce whatever quantity is demanded, the Cournot model (Cournot, 1838) assumes that firms determine the quantity that they want to sell to the market, and prices are subsequently determined based on a presumed process of market clearing.
This commentary first discusses the theoretical justifications behind the Cournot model relative to the Bertrand model, so as to subsequently link the respective models to their use in competition policy practice. For a comprehensive introduction to oligopoly theory more generally, see, for example, Shapiro (1989).
As discussed by Walker (no date), the basic Bertrand model of price competition with homogeneous products leads to the counterintuitive result that equilibrium prices will always be equal to marginal costs, and firms will never make any profit on their products sold. This is considered to be a paradox, as in reality we observe price-setting competitors enjoying positive gross margins. To resolve the paradox, the basic model would need to be extended by allowing for differentiated products, capacity limitations, long-run repeated interaction, or imperfect information.
In contrast, the basic Cournot model of quantity competition leads to the intuitive result that equilibrium prices are higher when markets are more concentrated. The basic intuition is as follows: the market-clearing price is inversely related to the total supply of a product in a particular market (higher total supply leads to a lower market prices, and lower total supply leads to higher market prices). When there are fewer firms active in a market, any one firm will have a larger influence on the market-clearing price. Each individual firm has a higher incentive to restrict its output somewhat in order to push up the market-clearing price. Conversely, when markets are less concentrated, each individual firm has a smaller incentive to restrict its output, as its influence on the market-clearing price is smaller. Equilibrium quantities are lower and market prices (and hence margins) higher in more concentrated markets. In fact, it can be shown that in a linear Cournot model with homogeneous products, the Hirschman-Herfindahl Index (HHI) for market concentration is one-to-one related to market power as measured by price-cost mark-ups (i.e. the Lerner Index)—justifying the use of HHI as a measure of market power in such cases.
Importantly, economic theory also shows that under relatively mild assumptions, the theoretical outcome under Cournot competition between firms mimics the theoretical outcome of a two-stage model in which firms first choose their capacity level of production and subsequently compete on price (Kreps and Scheinkman, 1983). As such, the Cournot model may still be a better reflection of market competition even if firms compete on price, provided that they first invest in a particular capacity level and cannot readily change these levels (so-called ‘capacity-then-price’ competition).
Bertrand and Cournot models of competition are used in the academic economics literature (theoretical and empirical) to analyse how different market characteristics or interventions may be expected to affect market outcomes. Similarly, these models are used in competition policy practice to provide economic insights on the potential effects of mergers, coordinated behavior, or unilateral conduct. For example, in complex merger cases, a Bertrand or Cournot model may be calibrated using real-world data on margins and diversion ratios to estimate the changes in the theorised equilibrium prices and output post-merger. Such an analysis combines economic theory with data to produce a type of economic evidence that may complement other evidence on the potential competitive effects of a merger (quantitative or qualitative). Bertrand and Cournot models are also used, for instance, in antitrust damages proceedings to help inform an economic expectation of harm following a cartel infringement.
To choose between a Bertrand or Cournot model of competition means to choose between two different ways in which firms are assumed to behave in the market. Bertrand competition is more appropriate when firms have unlimited capacity or when prices are difficult to adjust in the short run. In contrast, Cournot competition is more appropriate when firms can readily change prices but face capacity constraints that can only be adjusted in the longer run.
For example, in mobile telecommunication mergers, the European Commission consistently assumes that firms set prices without regard to any capacity constraints (i.e. Bertrand competition) - including, for example, in Hutchison 3G Austria / Orange Austria (2012), Hutchison 3G UK / Telefonica UK (2016), and T-Mobile NL / Tele2 NL (2018). This is appropriate, as network capacity is rarely binding for telecom operators and retail prices are usually fixed over the short run.
In contrast, an assumption that firms commit to prices while flexibly adjusting volume depending on demand may not be realistic in other settings. For example, in support of its Sunweb / Corendon (2020) merger clearance, the Netherlands Authority for Consumers & Markets (ACM) produced a merger simulation model for the market of packaged holidays that assumes that firms compete by setting quantities rather than price (i.e. Cournot competition). This choice was driven by the observation that firms active in the market for packaged holidays first stock up on flight and accommodation capacity for a subsequent season, based on estimated future demand, and then sell this fixed capacity to consumers against a dynamically optimised price aimed at fulfilling capacity. Such a competitive dynamic coincides with the capacity-then-price model discussed above.