Existence and properties of solutions to the generalized Nash equilibrium problem

A. V. Arutyunov^a, E. S. Zhukovskiy^b, S. E. Zhukovskiy<sup>a

a</sup> Trapeznikov Institute of Control Sciences, Moscow, Russia
^b Derzhavin Tambov State University, Tambov, Russia

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.

UDC: 519.83+517.988.38

MSC: 35R30

Received: 09.04.2025
Revised: 09.04.2025
Accepted: 19.06.2025

DOI: 10.33048/smzh.2025.66.502

 English version: Siberian Mathematical Journal, 2025, 66:5, 1116–1133