Distributed Nash Equilibrium Seeking for Aggregative Games With Linear Convergence Over Digraphs

Aggregative games over directed networks are considered in this paper, where each player aims to minimize its cost function related to its own decision variables and the aggregate of all the players’ decision variables. Taking advantage of the dynamic average consensus method to estimate the aggregative information which is unavailable for any player, we design a discrete-time algorithm with a fixed step-size over unbalanced directed networks with row-stochastic matrices. The proposed algorithm converges to the Nash equilibrium with a linear convergence rate given that cost functions are strongly convex and their pseudo-gradients are strongly monotone. In addition, the validity of the proposed algorithm is corroborated by numerical examples on heating ventilation air conditioning systems and Nash–Cournot games.