Monotone Operator Methods for Nash Equilibria in Non-Potential Games

TL;DR

This paper introduces monotone operator methods to find Nash equilibria in non-potential games, providing new splitting algorithms with proven convergence for various game types.

Contribution

It develops novel splitting techniques for monotone inclusion problems related to Nash equilibria in non-potential games, with convergence guarantees.

Findings

Effective algorithms for generalized Nash equilibria

Convergence proofs for proposed methods

Applications to zero-sum and cyclic proximity problems

Abstract

We observe that a significant class of Nash equilibrium problems in non-potential games can be associated with monotone inclusion problems. We propose splitting techniques to solve such problems and establish their convergence. Applications to generalized Nash equilibria, zero-sum games, and cyclic proximity problems are demonstrated.