## Abstract

We present an analysis of generalized Nash equilibrium problems in infinite-dimensional spaces with possibly non-convex objective functions of the players. Such settings arise, for instance, in games that involve nonlinear partial differential equation constraints. Due to non-convexity, we work with equilibrium concepts that build on first order optimality conditions, especially Quasi-Nash Equilibria (QNE), i.e. first-order optimality conditions for (Generalized) Nash Equilibria, and Variational Equilibria (VE), i.e. first-order optimality conditions for Normalized Nash Equilibria. We prove existence of these types of equilibria and study characterizations of them via regularized (and localized) Nikaido-Isoda merit functions. We also develop continuity and (continuous) differentiability results for these merit functions under quite weak assumptions, using a generalization of Danskin's theorem. They provide a theoretical foundation for, e.g. using globalized descent methods for computing QNE or VE.

Original language | English |
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Journal | Optimization Methods and Software |

DOIs | |

State | Accepted/In press - 2024 |

## Keywords

- (regularized) Nikaido–Isoda function
- 46N10
- 49J27
- 49J50
- 90C26
- 90C48
- 91A10
- Danskin's theorem
- Generalized Nash equilibrium problems
- existence of equilibria
- infinite-dimensional spaces
- merit functions