Simultaneous Best-Response Dynamics in Random Potential Games

16^th May 2025, 13:00 Ashton Lecture Theatre
Edward Plumb
LSE

Abstract

We examine the convergence behaviour of simultaneous best-response dynamics in random potential games. We provide a theoretical result showing that, for a sufficiently large number of 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, this fast convergence is robust, in the sense that it occurs in non-potential games, provided the players' payoffs are highly 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 substantially faster.