Distributed Best Response Algorithms for Potential Games

In this paper we design and analyze distributed algorithms to compute a Nash equilibrium in potential games. Our algorithms are based on best-response dynamics, with suitable revision sequences (orders of play). We compute the average complexity over all potential games of best response dynamics under a random i.i. d. revision sequence, since it can be implemented in a distributed way using Poisson clocks. We obtain a distributed algorithm whose execution time is within a constant factor of the optimal centralized one.We then show how to take advantage of the structure of the interactions between players in a network game: non-interacting players can play simultaneously. This improves best response algorithm, both in the centralized and in the distributed case.