Editing Oligopoly (section)

== Modeling oligopolies ==
There is no single model that describes the operation of an oligopolistic market.<ref name="Colander_288" /> The variety and complexity of the models exist because numerous firms can compete on the basis of price, quantity, technological innovations, marketing, and reputation. However, there are a series of simplified models that attempt to describe market behavior under certain circumstances. Some of the better-known models are the [[dominant firm model]], the [[Cournot–Nash model]], the [[Bertrand model]] and the [[kinked demand]] model. As different industries have different characteristics, oligopoly models differ in their applicability within each industry.

=== Game theoretical models ===
With few sellers, each oligopolist is likely to be aware of the actions of their competition. According to [[game theory]], the decisions of one firm influence, and are influenced by, the decisions of other firms. [[Strategic planning]] by oligopolists needs to take into account the likely responses of the other market participants. The following game-theoretical oligopoly models attempt to describe and predict the behaviour of oligopolies:
* Stackelberg's [[duopoly]]. In this model, the firms move sequentially to determine their quantities (see [[Stackelberg competition]]).
* Cournot's duopoly. In this model, the firms simultaneously choose quantities (see [[Cournot competition]]).
* Bertrand's oligopoly. In this model, the firms simultaneously choose prices (see [[Bertrand competition]]).

One major difference between varying industries is capacity constraints. Both Cournot model and Bertrand model consist of the two-stage game;{{Clarify|date=July 2023|reason=what's the two stage game?}} the Cournot model is more suitable for firms in industries that face capacity constraints, where firms set their quantity of production first, then set their prices. The Bertrand model is more applicable for industries with low capacity constraints, such as banking and insurance.<ref>{{cite book | doi=10.1017/CBO9780511804038 | title=Competition Policy | year=2004 | last1=Motta | first1=Massimo | isbn=9780521816632 }}</ref>

==== ''Cournot-Nash model'' ====
{{Main|Cournot competition}}

The [[Antoine Augustin Cournot|Cournot]]–[[John Nash (mathematician)|Nash]] model is the simplest oligopoly model. The model assumes that there are two equally positioned firms; the firms compete on the basis of quantity rather than price, and each firm makes decisions on the assumption that the other firm's behaviour is unchanging.<ref>This statement is the Cournot conjectures. Kreps, D.: A Course in Microeconomic Theory page 326. Princeton 1990.</ref> The market demand curve is assumed to be linear, and marginal costs constant.

In this model, the [[Nash equilibrium]] can be found by determining how each firm reacts to a change in the output of the other firm, and repeating this analysis until a point is reached where neither firm desires to act any differently, given their predictions of the other firm's responsive behaviour.<ref>Kreps, D. ''A Course in Microeconomic Theory''. page 326.  Princeton 1990.</ref>

The equilibrium is the intersection of the two firm's ''reaction functions'', which show how one firm reacts to the quantity choice of the other firm.<ref>Kreps, D. ''A Course in Microeconomic Theory''. Princeton 1990.{{page needed|date=September 2010}}</ref> The reaction function can be derived by calculating the first-order condition (FOC) of the firms' optimal profits. The FOC can be calculated by setting the first derivative of the objective function to zero. For example, assume that the firm <math>1</math>'s demand function is <math>P = (M - Q_2) - Q_1</math>, where <math>Q_2</math> is the quantity produced by the other firm , <math>Q_1</math> is the amount produced by firm <math>1</math>,<ref>Samuelson, W & Marks, S. ''Managerial Economics''. 4th ed. Wiley 2003{{page needed|date=September 2010}}</ref> and <math>M=60</math> is the market. Assume that marginal cost is <math>C_M=12</math>. By following the profit maximisation rule of equating marginal revenue to marginal costs,{{Clarify|date=July 2023|reason=unsure what this means; wikilink or explain}} firm <math>1</math> can obtain a total revenue function of <math>R_T = Q_1 P = Q_1 (M - Q_2 - Q_1) = MQ_1 - Q_1 Q_2 - Q_1^2</math>. The marginal revenue function is <math>R_M = \frac{\partial R_T}{\partial Q_1} = M - Q_2 - 2 Q_1</math>.<ref group="note"><math>R_M = M - Q_2 - 2Q_1</math>. can be restated as <math>R_M = (M - Q_2) - 2Q_1</math>.</ref>
:<math>R_M = C_M</math>
:<math>M - Q_2 - 2Q_1 = C_M</math>
:<math>2Q_1 = (M - C_M) - Q_2</math>
:<math>Q_1 = \frac{M - C_M}{2} - \frac{Q_2}{2} = 24 - 0.5 Q_2</math> [1.1]
:<math>Q_2 = 2(M - C_M) - 2Q_1 = 96 - 2Q_1</math> [1.2]

Equation 1.1 is the reaction function for firm <math>1</math>. Equation 1.2 is the reaction function for firm <math>2</math>. The Nash equilibrium can thus be obtained by solving the equations simultaneously or graphically.<ref>Pindyck, R & Rubinfeld, D: Microeconomics 5th ed. Prentice-Hall 2001{{page needed|date=September 2010}}</ref>

Reaction functions are not necessarily symmetric.<ref>Pindyck, R & Rubinfeld, D: Microeconomics 5th ed. Prentice-Hall 2001</ref> Firms may face differing cost functions, in which case the reaction functions and equilibrium quantities would not be identical.

==== ''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.

==== ''Cournot-Bertrand model'' ====
The Cournot model and Bertrand model are the most well-known models in oligopoly theory, and have been studied and reviewed by numerous economists.<ref name="Ma, Wang">{{cite journal |last1=Ma |first1=Junhai |last2=Wang |first2=Hongwu |date=2013 |title=Complexity Analysis of a Cournot-Bertrand Duopoly Game Model with Limited Information |journal=Discrete Dynamics in Nature and Society |volume=2013 |pages=6 |doi=10.1155/2013/287371 |doi-access=free}}</ref> The Cournot-Bertrand model is a hybrid of these two models and was first developed by Bylka and Komar in 1976.<ref name="Tremblay">{{cite journal |last1=Horton Tremblay |first1=Carol |last2=Tremblay |first2=Victor J. |date=2019 |title=Oligopoly Games and The Cournot–Bertrand Model: A Survey |journal=Journal of Economic Surveys |volume=33 |issue=5 |pages=1555–1577 |doi=10.1111/joes.12336 |s2cid=202322675}}</ref> This model allows the market to be split into two groups of firms. The first group's aim is to optimally adjust their output to maximise profits, while the second group's aim is to optimally adjust their prices.<ref name="Ma, Wang" /> This model is not accepted by some economists who believe that firms in the same industry cannot compete with different strategic variables.<ref name="Tremblay" /> Nonetheless, this model has been applied and observed in both real-world examples and theoretical contexts.

In the Cournot model and Bertrand model, it is assumed that all the firms are competing with the same choice variable, either output or price.<ref name="Tremblay" /> However, some economists have argued that this does not always apply in real world contexts. Economists Kreps and Scheinkman's research demonstrates that varying economic environments are required in order for firms to compete in the same industry while using different strategic variables.<ref name="Tremblay" /> An example of the Cournot-Bertrand model in real life can be seen in the market of alcoholic beverages.<ref name="Tremblay" /> The production times of alcoholic beverages differ greatly creating different economic environments within the market.<ref name="Tremblay" /> The fermentation of distilled spirits takes a significant amount of time; therefore, output is set by producers, leaving the market conditions to determine price.<ref name="Tremblay" /> Whereas, the production of brandy requires minimal time to age, thus the price is set by the producers and the supply is determined by the quantity demanded at that price.<ref name="Tremblay" />{{Clarify|date=July 2023|reason=unsure what this paragraph is trying to say}}

=== Kinked demand curve model ===
{{Main|Kinked demand}}
In an oligopoly, firms operate under [[imperfect competition]]. The fierce price competitiveness, created by a [[Sticky (economics)|sticky-upward]] [[demand curve]], causes firms to use [[non-price competition]] in order to accrue greater revenue and market share.

"Kinked" demand curves appear similar to traditional demand curves but are distinguished by a hypothesised{{Clarify|date=July 2023|reason=what does this mean?}} convex bend with a discontinuity at the bend–"kink". Thus, the first [[derivative]] at that point is undefined and leads to a jump discontinuity in the [[marginal revenue|marginal revenue curve]]. Because of this jump discontinuity in the marginal revenue curve, [[marginal cost]] could change without necessarily changing the price or quantity. The motivation behind the kink is that in an oligopolistic or monopolistic competitive market, firms will not raise their prices because even a small price increase will lose many customers. However, even a large price decrease will gain only a few customers because such an action will begin a [[price war]] with other firms. The curve is, therefore, more [[Elasticity (economics)|price-elastic]] for price increases and less so for price decreases. This model predicts that more firms will enter the industry in the long run, since market price for oligopolists is more stable.<ref name=":2" />

The kinked demand curve for a joint profit-maximizing oligopoly industry can model the behaviors of oligopolists' pricing decisions other than that of the price leader.[[File:Kinked demand.JPG|thumb|Above the kink, demand is relatively elastic because all other firms' prices remain unchanged. Below the kink, demand is relatively inelastic because all other firms will introduce a similar price cut, eventually leading to a [[price war]]. Therefore, the best option for the oligopolist is to produce at point <math>\text{E}</math> which is the equilibrium point and the kink point. This is a theoretical model proposed in 1947, which has failed to receive conclusive evidence for support.<ref name=":2">{{cite journal | doi=10.2307/1911701 | jstor=1911701 | title=A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles | last1=Maskin | first1=Eric | last2=Tirole | first2=Jean | journal=Econometrica | year=1988 | volume=56 | issue=3 | pages=571–599 }}</ref>]]

==== ''Assumptions'' ====
According to the kinked-demand model, each firm faces a demand curve kinked at the existing price.<ref name="Pindyck_446">Pindyck, R. & Rubinfeld, D. ''Microeconomics'' 5th ed. page 446. Prentice-Hall 2001.</ref> The assumptions of the model are:
* If a firm raises its price above the current existing price, competitors will not follow and the acting firm will lose market share.
* If a firm lowers prices below the existing price, their competitors will follow to retain their market share and the firm's output will increase only marginally.<ref>Simply stated the rule is that competitors will ignore price increases and follow price decreases. Negbennebor, A: Microeconomics, The Freedom to Choose page 299. CAT 2001</ref><ref>{{Citation |last1=Kalai |first1=Ehud |title=The Kinked Demand Curve, Facilitating Practices, and Oligopolistic Coordination |date=1994 |url=http://link.springer.com/10.1007/978-94-011-1370-0_2 |work=Imperfections and Behavior in Economic Organizations |volume=11 |pages=15–38 |editor-last=Gilles |editor-first=Robert P. |access-date=25 April 2021 |place=Dordrecht |publisher=Springer Netherlands |doi=10.1007/978-94-011-1370-0_2 |isbn=978-94-010-4599-5 |last2=Satterthwaite |first2=Mark A. |series=Theory and Decision Library |editor2-last=Ruys |editor2-first=Pieter H. M.}}</ref>

If the assumptions hold, then:
* The firm's marginal revenue curve is discontinuous and not differentiable, having a gap at the kink.<ref name="Pindyck_446" />
* For prices above the prevailing price, the curve is relatively elastic.<ref name="Negbennebor_299">Negbennebor, A. ''Microeconomics: The Freedom to Choose''. page 299. CAT 2001</ref>
* For prices below the point, the curve is relatively inelastic.<ref name="Negbennebor_299" />

The gap in the marginal revenue curve means that marginal costs can fluctuate without changing equilibrium price and quantity<ref name="Pindyck_446" /> Thus, prices tend to be rigid.

=== Other descriptions ===
[[Market power]] and [[market concentration]] can be estimated or quantified using several different tools and measurements, including the [[Lerner index]], [[stochastic frontier analysis]], New Empirical Industrial Organization (NEIO) modeling,<ref name="LopezHeAzzam" /> as well as the [[Herfindahl-Hirschman index]].<ref name="EricssonTegen" /> As a quantitative description of oligopoly, the four-firm [[concentration ratio]] is often utilised and is the most preferable ratio for analyzing [[market concentration]].<ref>Sys, C. (2009). Is the container liner shipping industry an oligopoly?. ''Transport Policy'', ''16''(5), 259-270.</ref> This measure expresses, as a percentage, the market share of the four largest firms in any particular industry. For example, as of fourth quarter 2008, the combined total market share of Verizon Wireless, AT&T, Sprint, and T-Mobile comprises 97% of the U.S. cellular telephone market.<ref>{{Cite web |last=Chitkara |first=Hirsh |title=US Cellular and Charter are challenging the Big Four's dominance in the US wireless market |url=https://www.businessinsider.com/us-cellular-charter-challenge-big-four-in-us-wireless-market-2019-10 |access-date=2023-04-09 |website=Business Insider |language=en-US |archive-date=19 April 2021 |archive-url=https://web.archive.org/web/20210419102843/https://www.businessinsider.com/us-cellular-charter-challenge-big-four-in-us-wireless-market-2019-10 |url-status=live }}</ref>