Distributed Nash equilibrium seeking: A gossip-based algorithm

This paper presents an asynchronous gossip-based algorithm for finding aNash equilibrium (NE) of a game in a distributedmulti-player network. The algorithm is designed in such away that playersmake decisions based on estimates of the other players’ actions obtained from local neighbors. Using a set of standard assumptions on the cost functions and communication graph, the paper proves almost sure convergence to a NE for diminishing step sizes. For constant step sizes an error bound on expected distance from a NE is established. The effectiveness of the proposed algorithm is demonstrated via simulation for both diminishing and constant step sizes. Crown Copyright© 2016 Published by Elsevier Ltd. All rights reserved.