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Avtomatika i Telemekhanika, 2022, Issue 8, Pages 140–158
DOI: https://doi.org/10.31857/S0005231022080086 (Mi at15881) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Control in Social Economic Systems

Analysis of equilibria in a nonlinear oligopoly model

M. I. Geraskin

Samara University, Samara, 443086 Russia
Full-text PDF (505 kB) First page Citations (6)
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DOI: https://doi.org/10.31857/S0005231022080086
Abstract: We consider the game-theoretic problem of choosing optimal strategies for agents of the oligopoly market for a linear demand function and nonlinear agent cost functions. A computational formula for the optimal action of an agent is derived in the form of a fractional irrational function; it is shown that the extrema of this function correspond to fixed points. To find a fixed point, an irrational equation is derived and approximate formulas for its solution are obtained. Necessary conditions for the existence and uniqueness or the multiplicity of equilibria depending on the agent type parameters are proved.
Keywords: oligopoly, aggregative game, fractional irrational function, fixed point, multiplicity of equilibria.
Presented by the member of Editorial Board: D. A. Novikov

Received: 28.01.2022
Revised: 15.04.2022
Accepted: 28.04.2022
English version:
Automation and Remote Control, 2022, Volume 83, Issue 8, Pages 1261–1277
DOI: https://doi.org/10.1134/S0005117922080082
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. I. Geraskin, “Analysis of equilibria in a nonlinear oligopoly model”, Avtomat. i Telemekh., 2022, no. 8, 140–158; Autom. Remote Control, 83:8 (2022), 1261–1277
Citation in format AMSBIB
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\by M.~I.~Geraskin
\paper Analysis of equilibria in a nonlinear oligopoly model
\jour Avtomat. i Telemekh.
\yr 2022
\issue 8
\pages 140--158
\mathnet{http://mi.mathnet.ru/at15881}
\crossref{https://doi.org/10.31857/S0005231022080086}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4486851}
\edn{https://elibrary.ru/AHSHBT}
\transl
\jour Autom. Remote Control
\yr 2022
\vol 83
\issue 8
\pages 1261--1277
\crossref{https://doi.org/10.1134/S0005117922080082}
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:30
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