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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2023, Volume 33, Issue 4, Pages 601–624
DOI: https://doi.org/10.35634/vm230405 (Mi vuu871) 		 
MATHEMATICS

Application of Lyapunov–Poincaré method of small parameter for Nash and Berge equilibrium designing in one differential two-player game

V. I. Zhukovskiia, L. V. Zhukovskayab, S. N. Sachkovc, E. N. Sachkovac

a Lomonosov Moscow State University, Leninskie Gory, 1, Moscow, 119991, Russia
b Central Economics and Mathematics Institute of the Russian Academy of Sciences, Nakhimovskii pr., 47, Moscow, 117418, Russia
c State University of Humanities and Technology, ul. Zelenaya, 22, Orekhovo-Zuevo, 142611, Russia
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DOI: https://doi.org/10.35634/vm230405
Abstract: The Poincaré small parameter method is actively used in celestial mechanics, as well as in the theory of differential equations and in its important section called optimal control. In this paper, the mentioned method is used to construct an explicit form of Nash and Berge equilibrium in a differential positional game with a small influence of one of the players on the rate of change of the state vector.
Keywords: small parameter method, differential linear-quadratic noncooperative game, Nash equilibrium, Berge equilibrium
Received: 14.09.2023
Accepted: 25.11.2023
Bibliographic databases:
Document Type: Article
UDC: 517.928.3, 519.62
MSC: 91A10
Language: English
Citation: V. I. Zhukovskii, L. V. Zhukovskaya, S. N. Sachkov, E. N. Sachkova, “Application of Lyapunov–Poincaré method of small parameter for Nash and Berge equilibrium designing in one differential two-player game”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 33:4 (2023), 601–624
Citation in format AMSBIB
\Bibitem{ZhuZhuSac23}
\by V.~I.~Zhukovskii, L.~V.~Zhukovskaya, S.~N.~Sachkov, E.~N.~Sachkova
\paper Application of Lyapunov–Poincar\'{e} method of small parameter for Nash and Berge equilibrium designing in one differential two-player game
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2023
\vol 33
\issue 4
\pages 601--624
\mathnet{http://mi.mathnet.ru/vuu871}
\crossref{https://doi.org/10.35634/vm230405}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=001145748100005}
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