Generalized Nash equilibrium seeking strategy for multi-cluster games

In this paper, multi-cluster games over weight-balanced digraphs are studied, where the cost functions of all players depend on not only their own decisions but also the decisions of players in other clusters. The cost functions of players are nonsmooth, and the decisions of all players are constrained by coupling constraints. In order to seek the variational generalized Nash equilibrium (GNE) of the multi-cluster games, we design an algorithm via gradient descent and differential inclusions, and its convergence to the variational GNE is proven with the help of Lyapunov stability theory and variational analysis.