Generalized Nash equilibrium seeking algorithm design for distributed multi-cluster games

In this article, we investigate multi-cluster games, where the cost functions of every player depends on its own decision as well as the decisions of players in other clusters. The decisions of players is constrained by not only local convex set constraints but also coupling constraints. For the purpose of seeking the variational generalized Nash equilibrium (GNE) of the multi-cluster game, we design a distributed algorithm by virtue of gradient descent and projections. Moreover, the asymptotical convergence of the algorithm to the variational GNE is analyzed with the help of Lyapunov stability theory and variational analysis. Finally, a simulation example is proposed to verify the validity of the algorithm. (c) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.