Distributed Nash Equilibrium Seeking for Aggregative Games via Derivative Feedback

In this paper, we investigate a continuous-time distributed Nash equilibrium seeking algorithm for a class of aggregative games, with application to the real-time pricing demand response. To seek the Nash equilibrium via local communication among neighbors, by combining projected gradient dynamics and consensus tracking dynamics, we propose a novel distributed algorithm for the players. We prove the convergence of the distributed algorithm via a constructed Lyapunov function and the variational inequality technique, and show an illustrative simulation related to the energy consumption control in smart grids.