Computing normalized Nash equilibria for generalized Nash games with nonconvex players

TL;DR

This paper introduces an exact method for computing normalized Nash equilibria in generalized Nash games with nonconvex players, extending existing approaches to nonconvex settings without convexity assumptions.

Contribution

It develops a novel method to find normalized Nash equilibria in nonconvex generalized games, expanding the scope of equilibrium computation techniques.

Findings

Method successfully finds NNE in several nonconvex games.

The approach works without convexity assumptions.

Demonstrates effectiveness on multiple nonconvex game examples.

Abstract

Generalized Nash equilibrium (GNE) is a solution concept for complete information games, in which each player's objective function and feasible region depend on other players' actions. While numerical methods for finding GNE when players possess convex structure are relatively mature, the same cannot be said when players optimize nonconvex objective functions over nonconvex feasible regions. Drawing inspiration from the notion of a normalized (or variational) Nash equilibrium, which is a more restrictive class of solutions to generalized Nash games, we extend the ideas of Harwood et al. ("Equilibrium modeling and solution approaches inspired by nonconvex bilevel programming." Computational Optimization and Applications, 87(2):641-676, 2024) to develop an exact method that can find a normalized Nash equilibrium (NNE) of a problem, when such an NNE exists. By adapting the framework of Harwood et al., we are able to find NNE without any convexity assumptions. We demonstrate the effectiveness of our method on several nonconvex games.