Evolution of mixed strategies in monotone games

TL;DR

This paper introduces continuous time flows for approximating Nash equilibria in monotone games and explores mean field equilibria in large symmetric games, demonstrating convergence under certain conditions.

Contribution

It presents novel continuous time dynamics for Nash equilibrium approximation in monotone games and extends the analysis to mean field equilibria in large player settings.

Findings

Convergence of continuous time flows to Nash equilibria in monotone games.

Approximation of mean field equilibria under monotonicity assumptions.

Applicability to large symmetric noncooperative games.

Abstract

We consider the basic problem of approximating Nash equilibria in noncooperative games. For monotone games, we design continuous time flows which converge in an averaged sense to Nash equilibria. We also study mean field equilibria, which arise in the large player limit of symmetric noncooperative games. In this setting, we will additionally show that the approximation of mean field equilibria is possible under a suitable monotonicity hypothesis.