Simultaneous Best-Response Dynamics in Random Potential Games

TL;DR

This paper studies the convergence of simultaneous best-response dynamics in random potential games, showing rapid convergence to cycles or equilibria, with robustness and advantages over gradient-based methods.

Contribution

It provides theoretical and empirical analysis of convergence behavior in multi-player potential and non-potential games, highlighting robustness and efficiency.

Findings

Converges quickly to 2-cycle in 2-player games with many actions.

Converges rapidly to Nash equilibrium in 3+ player games.

Robustness of results extends to non-potential games with correlated payoffs.

Abstract

This paper examines the convergence behaviour of simultaneous best-response dynamics in random 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.