Distributed dynamics for aggregative games: Robustness and privacy guarantees

Abstract

This paper considers the problem of Nash equilibrium (NE) seeking in aggregative games, where the cost function of each player depends on an aggregate of all players' actions. We present a distributed continuous-time algorithm such that the actions of the players converge to NE by communicating to each other through a connected network. As agents may deviate from their optimal strategies dictated by the NE seeking protocol, we investigate robustness of the proposed algorithm against time-varying disturbances. In particular, we provide rigorous robustness guarantees by proving input-to-state stability (ISS) and (Formula presented.) -stability properties of the NE seeking dynamics. A major concern in communicative schemes among strategic agents is that their private information may be revealed to other agents or to a curious third party who can eavesdrop the communications. Motivated by this, we investigate privacy properties of the algorithm and identify to what extent privacy is preserved when all communicated variables are compromised. Finally, we demonstrate practical applications of our theoretical findings on two case studies; namely, on an energy consumption game and a coordinated charging of electric vehicles.