Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2015, Volume 25, Issue 2, Pages 147–156
This article is cited in 2 scientific papers (total in 2 papers)
The Berge equilibrium in Cournot's model of oligopoly
V. I. Zhukovskiia, K. N. Kudryavtsevb, A. S. Gorbatova
a Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow, 119991, Russia
b Faculty of Mathematics, Mechanics and Computer Science, South Ural State University, pr. Lenina, 76, Chelyabinsk, 454080, Russia
In many large areas of the economy (such as metallurgy, oil production and refining, electronics), the main competition takes place among several companies that dominate the market. The first models of such markets — oligopolies were described more than a hundred years ago in articles by Cournot, Bertrand, Hotelling. Modeling of oligopolies continues in many modern works. Moreover, in 2014 Nobel Prize in Economics “for his analysis of market power and regulation in sectors with few large companies” was received by Jean Tirole — the author of one of the best modern textbooks on the theory of imperfect competition “The Theory of Industrial Organization”.
The main idea of all these publications, studying the behavior of oligopolies, is that every company is primarily concerned with its profits.
This approach meets the concept of Nash equilibrium and is actively used in modeling the behavior of players in a competitive market. The exact opposite of such “selfish” equilibrium is “altruistic” concept of Berge equilibrium.
In this approach, each player, without having to worry about himself, choose his actions (strategies) trying
to maximize the profits of all other market participants. This concept called Berge equilibrium appeared
in Russia in 1994 in reference to the France Claude Berge monograph published in 1957.
The first works on the concept of Berge equilibrium belong to K. S. Vaisman and V. I. Zhukovskii. Once outside Russia, the concept of “Berge equilibrium” is slowly gaining popularity.
To day, the number of publications related to this balance is already measured in tens. However,
all of these items are limited to purely theoretical issues, or, in general, to psychology applications.
Works devoted to the study of Berge equilibrium in economic problems, were not seen until now. It's probably a consequence of Martin Shubik's review (“…no attention is paid to the application to the economy. …the book is
of little interest for economists”) of the Berge's book, it “scared” economists for a long time.
However, it is not so simple. In this article, Berge equilibrium is considered in Cournot oligopoly,
its relation to Nash equilibrium is studied. Cases are revealed in which players gain more profit by following the concept of Berge equilibrium, than by using strategies dictated by Nash equilibrium.
Cournot's oligopoly, Berge equilibrium, Nash equilibrium, non-cooperative game.
PDF file (257 kB)
MSC: 91A10, 91B26
V. I. Zhukovskii, K. N. Kudryavtsev, A. S. Gorbatov, “The Berge equilibrium in Cournot's model of oligopoly”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 25:2 (2015), 147–156
Citation in format AMSBIB
\by V.~I.~Zhukovskii, K.~N.~Kudryavtsev, A.~S.~Gorbatov
\paper The Berge equilibrium in Cournot's model of oligopoly
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
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This publication is cited in the following articles:
Yu. A. Belskikh, V. I. Zhukovskii, S. P. Samsonov, “Altruisticheskoe ravnovesie (po Berzhu) v modeli duopolii Bertrana”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 26:1 (2016), 27–45
M. Larbani, V. I. Zhukovskii, “Berge equilibrium in normal form static games: a literature review”, Izv. IMI UdGU, 49 (2017), 80–110
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