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Avtomatika i Telemekhanika, 2022, Issue 3, Pages 84–109
DOI: https://doi.org/10.31857/S0005231022030072
(Mi at15909)
 

This article is cited in 13 scientific papers (total in 13 papers)

Control in Social Economic Systems

To the analytical investigation of the convergence conditions of the processes of reflexive collective behavior in oligopoly models

G. I. Algazina, J. G. Algazinab

a Altai State University, Barnaul, 656049 Russia
b Polzunov Altai State Technical University, Barnaul, 656038 Russia
References:
Abstract: A study of the dynamics of the collective behavior of interconnected rational agents under conditions of incomplete information is presented. Statements are proved that permit one to unify the conditions for convergence to equilibrium for two trajectories of the response of agents to the expected actions of the environment: (1) “classic” optimization behavior, in which agents try to choose optimal responses, ignoring possible current “negative states;” (2) behavior that guarantees each agent motion towards the objective and nonnegative current states. The application of the results obtained in the Cournot and Stackelberg oligopoly models with reflexive behavior of agents is shown. Sufficient conditions for the convergence of processes of collective behavior in an oligopoly with an arbitrary number of Stackelberg leaders are obtained.
Keywords: reflexive collective behavior, equilibrium, convergence condition, oligopoly model, incomplete awareness, analytical result.
Presented by the member of Editorial Board: M. V. Goubko

Received: 23.07.2020
Revised: 23.11.2021
Accepted: 24.12.2021
English version:
Automation and Remote Control, 2022, Volume 83, Issue 3, Pages 367–388
DOI: https://doi.org/10.1134/S0005117922030067
Document Type: Article
Language: Russian
Citation: G. I. Algazin, J. G. Algazina, “To the analytical investigation of the convergence conditions of the processes of reflexive collective behavior in oligopoly models”, Avtomat. i Telemekh., 2022, no. 3, 84–109; Autom. Remote Control, 83:3 (2022), 367–388
Citation in format AMSBIB
\Bibitem{AlgAlg22}
\by G.~I.~Algazin, J.~G.~Algazina
\paper To the analytical investigation of the convergence conditions of the processes of reflexive collective behavior in oligopoly models
\jour Avtomat. i Telemekh.
\yr 2022
\issue 3
\pages 84--109
\mathnet{http://mi.mathnet.ru/at15909}
\crossref{https://doi.org/10.31857/S0005231022030072}
\transl
\jour Autom. Remote Control
\yr 2022
\vol 83
\issue 3
\pages 367--388
\crossref{https://doi.org/10.1134/S0005117922030067}
Linking options:
  • https://www.mathnet.ru/eng/at15909
  • https://www.mathnet.ru/eng/at/y2022/i3/p84
  • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Avtomatika i Telemekhanika
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