In this paper we consider the problem of distributed Nash equilibrium (NE)seeking over networks, a setting in which players have limited localinformation. We start from a continuous-time gradient-play dynamics thatconverges to an NE under strict monotonicity of the pseudo-gradient and assumesperfect information, i.e., instantaneous all-to-all player communication. Weconsider how to modify this gradient-play dynamics in the case of partial, ornetworked information between players. We propose an augmented gradient-playdynamics with correction in which players communicate locally only with theirneighbours to compute an estimate of the other players' actions. We derive thenew dynamics based on the reformulation as a multi-agent coordination problemover an undirected graph. We exploit incremental passivity properties and showthat a synchronizing, distributed Laplacian feedback can be designed usingrelative estimates of the neighbours. Under a strict monotonicity property ofthe pseudo-gradient, we show that the augmented gradient-play dynamicsconverges to consensus on the NE of the game. We further discuss two cases thathighlight the tradeoff between properties of the game and the communicationgraph.
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