A distributed Bregman forward-backward algorithm for a class of Nash equilibrium problems

Abstract

We present a distributed Nash equilibrium seeking method based on the Bregman forward-backward splitting, which allows us to have a mirror mapping instead of the standard projection as the backward operator. Our main technical contribution is to show convergence to a Nash equilibrium when the game has cocoercive pseudogradient mapping. Furthermore, when the feasible sets of the agents are simplices, a suitable choice of a Legendre function results in an exponentiated pseudogradient method, which, in our numerical experience, performs out the standard projected pseudogradient and dual averaging methods.