Solving Monotone Variational Inequalities with Best Response Dynamics

TL;DR

This paper introduces a best response dynamics approach for solving monotone variational inequalities, extending to game theory and population games, and analyzes its robustness under disturbances.

Contribution

It develops a novel best response dynamics method for monotone variational inequalities, applicable to game theory and constrained population games, with robustness analysis.

Findings

Convergence to Nash equilibria in game settings.

Generalization of population games with convex constraints.

Robustness of the method under time-varying disturbances.

Abstract

We leverage best response dynamics to solve monotone variational inequalities on compact and convex sets. Specialization of the method to variational inequalities in game theory recovers convergence results to Nash equilibria when agents select the best response to the current distribution of strategies. We apply the method to generalize population games with additional convex constraints. Furthermore, we explore the robustness of the method by introducing various types of time-varying disturbances.