Distributed Nash equilibrium seeking in networked graphical games

Abstract

This paper considers a gossip approach for finding a Nash equilibrium in networked games on graphs, where a player’s cost function may be affected by the actions of any subset of players. An interference graph illustrates the partially-coupled cost functions, i.e., the asymmetric strategic interaction and information requirements. An algorithm is proposed whereby players make decisions based only on the estimates of their interfering players’ actions. Given the interference graph (not necessarily complete), a communication graph is designed so that players exchange only their required information. When the interference graph is sparse, the algorithm can offer substantial savings in communication and computation. Almost sure convergence to a Nash equilibrium is proved for diminishing step sizes. The effect of the second largest eigenvalue of the expected communication matrix on the convergence rate is quantified.