Nash equilibrium seeking by a gossip-based algorithm

In this paper an asynchronous gossip-based algorithm is proposed for finding a Nash equilibrium of a game in a distributed multi-player network. The algorithm is designed in such a way that the players´ actions are updated based on the estimates of the other players´ actions which are obtained from the local neighbors. The almost sure convergence proof of the algorithm to a Nash equilibrium is provided under a set of standard assumptions on the cost functions and the communication graph. The effectiveness of the proposed algorithm is demonstrated via simulation.