Editing Oligopoly (section)

==== ''Bertrand model'' ====
The Bertrand model is essentially the Cournot–Nash model, except the strategic variable is price rather than quantity.<ref name="Samuelson_415">Samuelson, W. & Marks, S. ''Managerial Economics''. 4th ed. page 415 Wiley 2003.</ref>{{Clarify|date=July 2023|reason=unsure what 'strategic variable' means; wikilink, wiktionary or explain}}

Bertrand's model assumes that firms are selling homogeneous products and therefore have the same marginal production costs, and firms will focus on competing in prices simultaneously. After competing in prices for a while, firms would eventually reach an equilibrium where prices would be the same as marginal costs of production. The mechanism behind this model is that even by undercutting just a small increment of its price, a firm would be able to capture the entire market share. Even though empirical studies suggest that firms can easily make much higher profits by agreeing on charging a price higher than marginal costs, highly rational firms would still not be able to stay at a price higher than marginal cost. Whilst Bertrand price competition is a useful abstraction of markets in many settings, due to its lack of ability to capture human behavioural patterns, the approach has been criticised for being inaccurate in predicting prices.<ref>{{cite journal | doi=10.4284/0038-4038-2012.264 | title=A Psychological Reexamination of the Bertrand Paradox | year=2014 | last1=Fatas | first1=Enrique | last2=Haruvy | first2=Ernan | last3=Morales | first3=Antonio J. | journal=Southern Economic Journal | volume=80 | issue=4 | pages=948–967 }}</ref>

The model assumptions are:
* There are two firms in the market
* They produce a homogeneous product
* They produce at a constant marginal cost
* Firms choose prices <math>P_A</math> and <math>P_B</math> simultaneously
* Firms outputs are perfect substitutes
* Sales are split evenly if <math>P_A = P_B</math><ref>There is nothing to guarantee an even split. Kreps, D.: A Course in Microeconomic Theory page 331. Princeton 1990.</ref>

The only Nash equilibrium is <math>P_A = P_B = \text{MC}</math>. In this situation, if a firm raises prices, it will lose all its customers. If a firm lowers price, <math>P < \text{MC}</math>, then it will lose money on every unit sold.<ref>This assumes that there is no capacity restriction. Binger, B & Hoffman, E, 284–85. Microeconomics with Calculus, 2nd ed. Addison-Wesley, 1998.</ref>

The Bertrand equilibrium is the same as the competitive result.<ref>Pindyck, R & Rubinfeld, D: Microeconomics 5th ed.page 438 Prentice-Hall 2001.</ref>{{Clarify|date=July 2023|reason=unsure what 'competitive result' means; wikilink, wiktionary or explain}} Each firm produces where <math>P = \text{MC}</math>, resulting in zero profits.<ref name="Samuelson_415" /> A generalization of the Bertrand model is the [[Bertrand–Edgeworth model]], which allows for capacity constraints and a more general cost function.