ECONOMICS
A Comparison of the Cournot and Bertrand Model for Oligopolies
A short review I wrote at Imperial College discussing Cournot Competition and some alternative models, dated 18 November 2020.
Note: This review was written in conjuction with Adam Wood, Amalie Kjaer, Bastian Shi, Henry Jones and Tom O’Brien.
In the context of an oligopolistic market with identical goods, firms can yield the maximum profit by colluding to operate as a monopoly. However, competition law and the incentive to cheat cause significantly different behaviour [1]. The Cournot model describes this behaviour by stating that firms independently and simultaneously decide their respective supply based on competition output, with price being determined by the total supply in the market.
In industries where supply is difficult to adjust, such as cast-iron piping and records production [2], Cournot tends to model well, and the Nash equilibrium predicts companies generating supernormal profits. However, there are inherent assumptions that are not always applicable: that firms produce identical products, no collusion occurs, and decisions are made independently and simultaneously [3]. Consequently, other models have been developed to address the shortcomings of the Cournot model.
The Bertrand model assumes that firms compete on price rather than quantity and that customers will always purchase the cheaper good [4]. The model predicts that a duopoly is sufficient to push prices down to marginal cost suggesting a duopoly will always result in perfect competition (e.g., Coca-Cola and Pepsi)5. The model provides an incentive to collude to raise profits, but the Nash equilibrium occurs when the price is equal to marginal cost.
Although the Bertrand model contradicts Cournot, neither model is completely accurate as they are upheld by weak assumptions. The assumption that 100% of consumers would buy the cheaper alternative in the Bertrand model does not consider factors such as product accessibility. Cournot assumes the firms set their quantity independently which is equally unrealistic.
More complex dynamic models have been suggested which seem to more closely match real-world oligopolies [6]. A study done on 70 Japanese manufacturing industries found that the Cournot model was most likely for only 5 industries, while the Bertrand model was more apt for 35 industries, with the remaining 30 industries better described by hybrid models [2]. Some examples of hybrid models include:
- the Bertrand-Edgeworth model, where a limit to the willingness and ability of each firm’s supply exists [7],
- the Stackelberg model, which assumes firms decide on output quantity sequentially instead of simultaneously [8], and
- the two-stage Cournot-Bertrand model, which assumes firm choose capacities before competing in a Bertrand fashion [9].
How well a model describes behaviour depends on industry conditions, and therefore one must carefully consider the assumptions before implementation.
[1] En.wikipedia.org., 2020, “OPEC”. https://en.wikipedia.org/wiki/OPEC
[2] Flath, D., 2010, “Are There Any Cournot Industries?” https://www.iser.osaka-u.ac.jp/library/dp/2010/DP0766.pdf
[3] Liberto, D., 2019, “Cournot Competition” https://www.investopedia.com/terms/c/cournot-competition.asp#citation-2
[4] Pettinger, T., 2019, “Bertrand Competition” https://www.economicshelp.org/blog/glossary/bertrand-competition/
[5] Nadav, U., Piliouras, G., 2010, “No Regret Learning in Oligopolies: Cournot vs. Bertrand” https://link.springer.com/chapter/10.1007/978-3-642-16170-4_26
[6] Judd, K., 1989, “Cournot Versus Bertrand: A Dynamic Resolution” https://web.stanford.edu/~judd/papers/invold.pdf
[7] En.wikipedia.org., 2020, “Bertrand–Edgeworth model”. https://en.wikipedia.org/wiki/Bertrand%E2%80%93Edgeworth_model#:~:text=In%20microeconomics%2C%20the%20Bertrand%E2%80%93Edgeworth,sell%20at%20a%20particular%20price.
[8] Obaidullah, J., 2019, ” Oligopoly Models” https://xplaind.com/594955/oligopoly-models
[9] En.wikipedia.org., 2020, ”Cournot competition”. https://en.wikipedia.org/wiki/Cournot_competition
