Title: A Passivity-Based Approach to Nash Equilibrium Seeking over Networks,
Abstract: In this paper we consider the problem of distributed Nash equilibrium (NE)
seeking over networks, a setting in which players have limited local
information. We start from a continuous-time gradient-play dynamics that
converges to an NE under strict monotonicity of the pseudo-gradient and assumes
perfect information, i.e., instantaneous all-to-all player communication. We
consider how to modify this gradient-play dynamics in the case of partial, or
networked information between players. We propose an augmented gradient-play
dynamics with correction in which players communicate locally only with their
neighbours to compute an estimate of the other players' actions. We derive the
new dynamics based on the reformulation as a multi-agent coordination problem
over an undirected graph. We exploit incremental passivity properties and show
that a synchronizing, distributed Laplacian feedback can be designed using
relative estimates of the neighbours. Under a strict monotonicity property of
the pseudo-gradient, we show that the augmented gradient-play dynamics
converges to consensus on the NE of the game. We further discuss two cases that
highlight the tradeoff between properties of the game and the communication
graph.