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.