  This paper considers the problem of Nash equilibrium (NE) seeking in
aggregative games, where the payoff 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. 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. We address this concern for the presented algorithm and show
that private information of the players cannot be reconstructed even if all the
communicated variables are compromised. 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) properties of the NE seeking dynamics. Finally, we demonstrate
practical applications of our theoretical findings on two case studies; namely,
on an energy consumption game and a charging coordination problem of electric
vehicles.
