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Sibirskii Matematicheskii Zhurnal, 2025, Volume 66, Number 5, Pages 789–810
DOI: https://doi.org/10.33048/smzh.2025.66.502 (Mi smj7978) 		 
Existence and properties of solutions to the generalized Nash equilibrium problem

A. V. Arutyunova, E. S. Zhukovskiyb, S. E. Zhukovskiya

a Trapeznikov Institute of Control Sciences, Moscow, Russia
b Derzhavin Tambov State University, Tambov, Russia
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DOI: https://doi.org/10.33048/smzh.2025.66.502
Abstract: The existence of Nash equilibrium in a game with two or more players is studied. The strategies of each player are elements of a noncompact metric space. Mixed constraints on strategies are considered, i.e., the set of admissible strategies of each participant may depend on the set of strategies of the other participants. Sufficient conditions for the existence of a solution to the generalized Nash equilibrium problem are obtained. Weak solutions to this problem are introduced and their properties are studied.
Keywords: generalized Nash equilibrium problem, Nikaido–Isoda function, constrained minimization, Caristi-like condition.
Funding agency Grant number
Russian Science Foundation 24-21-00272
The research was supported by the Russian Science Foundation (Project 24–21–00272, https://rscf.ru/project/24-21-00272/).
Received: 09.04.2025
Revised: 09.04.2025
Accepted: 19.06.2025
English version:
Siberian Mathematical Journal, 2025, Volume 66, Issue 5, Pages 1116–1133
DOI: https://doi.org/10.1134/S0037446625050027
Document Type: Article
UDC: 519.83+517.988.38
MSC: 35R30
Language: Russian
Citation: A. V. Arutyunov, E. S. Zhukovskiy, S. E. Zhukovskiy, “Existence and properties of solutions to the generalized Nash equilibrium problem”, Sibirsk. Mat. Zh., 66:5 (2025), 789–810; Siberian Math. J., 66:5 (2025), 1116–1133
Citation in format AMSBIB
\Bibitem{AruZhuZhu25}
\by A.~V.~Arutyunov, E.~S.~Zhukovskiy, S.~E.~Zhukovskiy
\paper Existence and properties of solutions to~the~generalized Nash equilibrium problem
\jour Sibirsk. Mat. Zh.
\yr 2025
\vol 66
\issue 5
\pages 789--810
\mathnet{http://mi.mathnet.ru/smj7978}
\transl
\jour Siberian Math. J.
\yr 2025
\vol 66
\issue 5
\pages 1116--1133
\crossref{https://doi.org/10.1134/S0037446625050027}
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    		Сибирский математический журнал Siberian Mathematical Journal
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