Simultaneous Best-Response Dynamics in Random Potential Games

Domenico Mergoni Cecchelli, Edward Plumb, Galit Ashkenazi-Golan

Keywords: Potential Games, Best-Response Dynamics, Multi-agent Learning, Algorithmic Game Theory

TL;DR: Does simultaneous Best-Response outperform Policy Gradient in near-potential random games?

Abstract:

This paper examines the convergence behaviour of simultaneous best-response dynamics in random potential games and random near-potential games. We provide a theoretical result showing that, for two-player games with sufficiently many actions, the dynamics converge quickly to a cycle of length two. This cycle lies within the intersection of the neighbourhoods of two distinct Nash equilibria. For three players or more, simulations show that the dynamics converge quickly to a Nash equilibrium with high probability. Furthermore, we show that all these results are robust, in the sense that they hold in non-potential games, provided the players' payoffs are sufficiently correlated.
We also compare these dynamics to gradient-based learning methods in near-potential games with three players or more, and observe that simultaneous best-response dynamics converge to a Nash equilibrium of comparable payoff substantially faster.

Primary Area: learning theory

Submission Number: 17564