Nash Equilibrium Seeking Over Undirected Graphs Via Multi-Agent Agreement

We consider the problem of distributed Nash equilibrium seeking over networks. In this setting, agents have limited information about the other players' actions and are forced to communicate with neighbouring agents. We start with a continuous-time gradient-play dynamics, with perfect information, under a strictly monotone pseudo-gradient assumption. In the partial information case we modify the gradient-play dynamics between players by expanding the action space. We propose an augmented gradient-play dynamics in which players can only communicate locally with their neighbours to compute an estimate of the other players' actions. We derive new dynamics based on the reformulation of the problem as a multi-agent coordination problem, over an undirected graph. We exploit the incremental passivity properties in the dynamics and show that a Laplacian feedback can be designed using relative estimates of their neighbours. We highlight that there is a trade-off between properties of the game and the communication graph.M.A.S