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Russia Moscow; Orekhovo-Zuevo
Year
2023
Volume
33
Issue
4
Pages
601–624
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Section Mathematics
Title Application of Lyapunov–Poincaré method of small parameter for Nash and Berge equilibrium designing in one differential two-player game
Author(-s) Zhukovskii V.I.a, Zhukovskaya L.V.b, Sachkov S.N.c, Sachkova E.N.c
Affiliations Lomonosov Moscow State Universitya, Central Economics and Mathematics Institute, Russian Academy of Scienceb, Moscow State Regional Institute of Humanities (State University of Humanities and Technology)c
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
UDC 517.928.3, 519.62
MSC 91A10
DOI 10.35634/vm230405
Received 14 September 2023
Language English
Citation Zhukovskii V.I., Zhukovskaya L.V., Sachkov S.N., Sachkova E.N. Application of Lyapunov–Poincaré method of small parameter for Nash and Berge equilibrium designing in one differential two-player game, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2023, vol. 33, issue 4, pp. 601–624.
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