Duopoly#Politics

In 1838, Antoine Augustin Cournot published a book titled "Researches Into the Mathematical Principles of the Theory of Wealth" in which he introduced and developed this model for the first time. As an imperfect competition model, Cournot duopoly (also known as Cournot competition), in which two firms with identical cost functions compete with homogenous products in a static context, is also known as Cournot competition.{{Cite journal |last1=Tremblay |first1=Carol Horton |last2=Tremblay |first2=Victor J. |date=June 2011 |title=The Cournot–Bertrand model and the degree of product differentiation |journal=Economics Letters |volume=111 |issue=3 |pages=233–235 |doi=10.1016/j.econlet.2011.02.011 |issn=0165-1765}} The Cournot model, shows that two firms assume each other's output and treat this as a fixed amount, and produce in their own firm according to this. The Cournot duopoly model relies on the following assumptions:{{Cite book |last=Dranove |first=David |title=Economics of Strategy |publisher=Hoboken:Wiley |year=2016 |edition=7th}}

• Each firm chooses a quantity to produce independently
• All firms make this choice simultaneously
• The cost structures of the firms are public information

In this model, two companies, each of which chooses its own quantity of output, compete against each other while facing constant marginal and average costs.{{Cite journal |last=Symeonidis |first=George |date=January 2003 |title=Comparing Cournot and Bertrand equilibria in a differentiated duopoly with product R&D |journal=International Journal of Industrial Organization |volume=21 |issue=1 |pages=39–55 |doi=10.1016/S0167-7187(02)00052-8 |issn=0167-7187}} The market price is determined by the sum of the output of two companies. $P(Q)=a-bQ$ is the equation for the market demand function.{{cite book|title=Recherches surplus Principes Mathématiques de la Théorie des Richesses|trans-title=Researches Into the Mathematical Principles of the Theory of Wealth|last=Cournot|first=Antoine Augustin|author-link=Antoine Augustin Cournot|translator-last=Bacon|translator-first=Nathaniel T.|date=1897|orig-date=Originally published 1838|publisher=The Macmillan Company|location=New York|url=https://books.google.com/books?id=eGgPAAAAYAAJ|hdl=2027/hvd.32044024354821|access-date=January 18, 2023}}

• Market with two firms {{math|1= i = 1, 2}} with constant marginal cost {{mvar|c{{sub|i}}}}
• Inverse market demand for a homogeneous good: {{math|1= P(Q) = a − bQ}}
• Where {{mvar|Q}} is the sum of both firms' production levels: {{math|1= Q = q{{sub|1}} + q{{sub|2}}}}
• Firms choose their quantity simultaneously (static game)
• Firms maximize their profit:

$$\backslash begin\{aligned\}$$

\Pi_1(q_1,q_2) &= \left(P(q_1 + q_2) - c_1\right)*q_1\,, \\

\Pi_2(q_1,q_2) &= \left(P(q_1 + q_2) - c_2\right)*q_2

\end{aligned}

The general process for obtaining a Nash equilibrium of a game using the best response functions is followed in order to discover a Nash equilibrium of Cournot's model for a specific cost function and demand function. A Nash Equilibrium of the Cournot model is a {{nowrap|($q\_1^*,\; q\_2^*$)}} such that

For a given {{nowrap|$q\_1^*$,}} $q\_2^*$ solves:

According to the Cournot model, firms in a duopoly would be able to keep prices above marginal cost and hence be extremely profitable.{{Cite journal |last=Vives |first=Xavier |author-link=Xavier Vives |date=October 1984 |title=Duopoly information equilibrium: Cournot and bertrand |journal=Journal of Economic Theory |volume=34 |issue=1 |pages=71–94 |doi=10.1016/0022-0531(84)90162-5 |issn=0022-0531}} Bertrand took issue with this. In this market structure, each firm could only choose whole amounts and each firm receives zero payoffs when the aggregate demand exceeds the size of the amount that they share with each other. The market demand function is $Q(P)=a-bP$. The Bertrand model has similar assumptions to the Cournot model:

• Two firms
• Homogeneous products
• Both firms know the market demand curve
• However, unlike the Cournot model, it assumes that firms have the same MC. It also assumes that the MC is constant.

The Bertrand model, in which, in a game of two firms, competes in price instead of output. Each one of them will assume that the other will not change prices in response to its price cuts. When both firms use this logic, they will reach a Nash equilibrium.

• Consider price competition among two firms ({{math|1=i = 1, 2}}) selling homogeneous good
• Downward sloping market demand {{math|D(p)}}, with {{math|{{prime|D}}(p) < 0}}
• Constant, symmetric marginal cost {{math|1= c{{sub|1}} = c{{sub|2}} = c}}
• Static game: firms set prices simultaneously
• Rationing rule of demand:

1. lowest priced firm wins all demand at its price
2. if prices are tied, each firm gets half of market demand at this price

• Firm {{mvar|i}}{{'}}s profits: $\backslash Pi\_i\; =\; (p\_i-c)D\_i(p\_i,\; p\_j)$

Let {{mvar|p{{sup|m}}}} be the monopoly price, $p^m\; =\; \backslash operatorname\{argmax\}\_p(p-c)D(p)$

• Firm {{mvar|i}}{{'}}s best response {{math|R{{sub|i}}(p{{sub|j}})}} is:

A commonly cited example of a duopoly is that involving Visa and Mastercard, who between them control a large proportion of the electronic payment processing market. In 2000 they were the defendants in a United States Department of Justice antitrust lawsuit.{{cite web|url=https://www.justice.gov/atr/case-document/file/992401/download|title=Complaint for Equitable Relief for Violations of 15 U.S.C. § 1: U.S. v. Visa U.S.A., et al.|format=PDF|publisher=U.S. Department of Justice|website=justice.gov|date=October 7, 1998|access-date=January 18, 2023}}{{cite journal|url=http://mit.edu/thistle/www/v12/2/credit.html|date=July 4, 2000|archive-url=https://web.archive.org/web/20020902064409/http://mit.edu/thistle/www/v12/2/credit.html|archive-date=September 2, 2002|title=Credit Card Antitrust Suit|journal=The Thistle|volume=12|number=2|access-date=January 18, 2023}} An appeal was upheld in 2004.{{cite news|url=http://news.bbc.co.uk/1/hi/business/4014599.stm|title=Amex is suing Visa and Mastercard|date=November 15, 2004|access-date=January 18, 2023|work=BBC News}}

Examples where two companies control an overwhelming proportion of a market are:

• Airbus and Boeing in the largest commercial aircraft market in the world
• Nvidia (who acquired competitor 3dfx in 2002) and AMD (formerly ATI which AMD acquired in 2006) in the GPU market
• Intel and AMD in the desktop CPU market
• Google's Android and Apple's iOS make up over 99% of the mobile operating system market{{cite news|url=https://www.theverge.com/2017/2/16/14634656/android-ios-market-share-blackberry-2016|title=99.6 percent of new smartphones run Android or iOS|last=Vincent|first=James|work=The Verge|date=February 16, 2017|access-date=January 18, 2023}}{{Cite web|title=Mobile Operating System Market Share Worldwide|url=https://gs.statcounter.com/os-market-share/mobile/worldwide|access-date=January 18, 2023|publisher=StatCounter|website=gs.statcounter.com}}
• Coca-Cola and Pepsi in the soft drink market, resulting in the cola wars. The two companies control nearly all of the cola beverage market.
• DC and Marvel in the American comic book market and movies{{cite web|last=Miller|first=John Jackson|author-link=John Jackson Miller|title=2017 Comic Book Sales to Comics Shops|url=http://www.comichron.com/monthlycomicssales/2017.html|website=Comichron|access-date=January 23, 2018|quote=Share of Overall Units—Marvel 38.30%, DC 33.93%; Share of Overall Dollars—Marvel 36.36%, DC 30.07%|archive-url=https://web.archive.org/web/20180123131602/http://www.comichron.com/monthlycomicssales/2017.html|archive-date=January 23, 2018|url-status=live}}{{cite news|title=Big Two Comic Publishers Lose Share|url=http://icv2.com/articles/comics/view/27580/big-two-comic-publishers-lose-share|access-date=September 22, 2015|work=ICv2|date=January 8, 2014|archive-url=https://web.archive.org/web/20160205190619/http://icv2.com/articles/comics/view/27580/big-two-comic-publishers-lose-share|archive-date=February 5, 2016|url-status=live}}
• Woolworths and Coles in the Australian supermarket market
• Walmart and Target in the American supermarket market
• Myer and David Jones in the Australian upmarket department store market
• Ford Australia and GM Holden in the Australian automotive industry{{Cite news |last=Nicastri |first=Timothy |date=2017-10-04 |title=Ford v Holden: What's behind this uniquely Australian rivalry? |url=https://www.abc.net.au/news/2017-10-05/ford-vs-holden-whats-behind-this-uniquely-australian-rivalry/9013842 |url-status=live |archive-url=https://web.archive.org/web/20180929115056/http://www.abc.net.au/news/2017-10-05/ford-vs-holden-whats-behind-this-uniquely-australian-rivalry/9013842 |archive-date=2018-09-29 |access-date=2025-04-12 |work=ABC News}}
• Husqvarna and Stihl in the chainsaw market
• World Wrestling Entertainment (then World Wrestling Federation) and World Championship Wrestling in the professional wrestling industry of the 1980s and 90s, resulting in the Monday Night Wars
• Windows and macOS in the desktop operating system (OS) market.
• Kesko and S Group together hold a 85% market share of grocery stores in Finland.{{Cite web |date=2017 |title=Päivittäistavarakaupan Duopoli-asetelma Suomessa |trans-title=Duopoly in Finnish Grocery Trade |url=https://www.theseus.fi/bitstream/handle/10024/138392/Toivanen_Kai.pdf;jsessionid=761F09EB2D959564DADA7E2F99DC5570?sequence=2}}{{Cite web |title=S-Group & Kesko with bigger combined share online than offline |url=https://adainsights.com/blog/s-group-amp-kesko-with-bigger-combined-share-online-than-offline |access-date=2024-12-04 |website=Ada Insights |language=en-US}}
• Christie's and Sotheby's sell more than 80% of works priced over $1m at auction.{{Cite web |date=2018 |title=Why the Christie's and Sotheby's duopoly is impregnable|url=https://www.theartnewspaper.com/2018/11/22/why-the-christies-and-sothebys-duopoly-is-impregnable}}

In Finland, the state-owned broadcasting company Yleisradio and the private broadcaster Mainos-TV had a legal duopoly (in the economists' sense of the word) from the 1950s to 1993. No other broadcasters were allowed. Mainos-TV operated by leasing air time from Yleisradio, broadcasting in reserved blocks between Yleisradio's own programming on its two channels. This was a unique phenomenon in the world. Between 1986 and 1992 there was an independent third channel but it was jointly owned by Yle and M-TV; only in 1993 did M-TV get its own channel.

In Kenya, mobile service providers Safaricom and Airtel in Kenya form a duopoly in the Kenyan telecommunications industry.

In Singapore, the mass media industry is presently dominated by two players, namely Mediacorp and SPH Media Trust.{{cite news |title=Singapore profile - Media |url=https://www.bbc.com/news/world-asia-15966553 |access-date=2 August 2023 |work=BBC News |publisher=British Broadcasting Corporation |date=23 May 2023 |language=en}}

In the United Kingdom, the BBC and ITV formed an effective duopoly (with Channel 4 originally being economically dependent on ITV) until the development of multichannel from the 1990s onwards.

{{Main|Duopoly (broadcasting)}}

Duopoly is used in the United States broadcast television and radio industry to refer to a single company owning two outlets in the same city. This usage is technically incompatible with the normal definition of the word and may lead to confusion, inasmuch as there are generally more than two owners of broadcast television stations in markets with broadcast duopolies. In Canada, this definition is therefore more commonly called a "twinstick".

{{Portal|Business}}

{{Wiktionary}}

• Monopoly
• Oligopoly
• Two-party system

{{Reflist}}

{{microeconomics}}

{{Authority control}}

Category:Market structure

Category:Oligopoly