Discrete-time algorithm for distributed Nash equilibrium seeking of a class of aggregative games

In this paper, we investigate a distributed Nash equilibrium seeking problem for aggregative games with nonlinear aggregation generators. In our game model, the strategic interaction is associated with a sum of heterogeneous nonlinear mapping of local decisions, and the local cost functions are non-quadratic with the decision variables limited in local constraint sets. We propose a novel discrete-time distributed equilibrium seeking algorithm based on dynamic average consensus protocal and projected gradient flows. By virtue of variational inequalities and Lyapunov functions, we show that the algorithm can achieve the Nash equilibrium for the distributed aggregative game.