Distributed Nash Equilibrium Seeking in Non-Monotone Games over the Simplex

TL;DR

This paper introduces distributed heuristic algorithms for approximating Nash equilibria in convex non-monotone games over the simplex by regularizing utilities with Shannon entropy and analyzing stationary points.

Contribution

It provides a novel characterization of approximate Nash equilibria in convex games over the simplex using entropy regularization and develops distributed algorithms based on this theory.

Findings

Algorithms effectively compute approximate Nash equilibria

Regularization links solutions to true Nash equilibria

Distributed approach scales to large games

Abstract

In this work, we present a novel characterization of approximate Nash equilibria in a class of convex games over the simplex. To achieve this, we regularize the utility functions using the Shannon entropy term, connect the solutions to the regularized game with the set of Nash equilibria, and formulate a multi-objective optimization problem to solve the regularized game. Based on the obtained properties of the stationary points in this optimization problem, we formulate two distributed heuristic algorithms to compute an approximate Nash equilibrium of the original game.