On Best-Response Dynamics in Potential Games

TL;DR

This paper analyzes the convergence behavior of continuous best-response dynamics in potential games, demonstrating that they typically have unique solutions and exponentially converge to pure Nash equilibria from almost all initial conditions.

Contribution

It provides new theoretical insights into the convergence properties of best-response dynamics in potential games, including uniqueness and exponential convergence.

Findings

Almost every potential game has unique best-response solutions.

Best-response dynamics converge to pure Nash equilibria from almost all initial states.

Convergence occurs at an exponential rate.

Abstract

The paper studies the convergence properties of (continuous) best-response dynamics from game theory. Despite their fundamental role in game theory, best-response dynamics are poorly understood in many games of interest due to the discontinuous, set-valued nature of the best-response map. The paper focuses on elucidating several important properties of best-response dynamics in the class of multi-agent games known as potential games---a class of games with fundamental importance in multi-agent systems and distributed control. It is shown that in almost every potential game and for almost every initial condition, the best-response dynamics (i) have a unique solution, (ii) converge to pure-strategy Nash equilibria, and (iii) converge at an exponential rate.