Distributed Generalized Nash Equilibria Seeking for Aggregative Games with Community Structures

This paper investigates the problem of seeking distributed generalized Nash equilibria (GNE) for aggregative games with community structures. The considered systems comprise agents that are interconnected through a two-scale hierarchical structure. At the lower level, agents are organized into group structures and are governed by upper-level agents, which collectively form the upper-level regulatory network. The decision variables of the two-level agents are interdependent. To address this game, we propose a distributed algorithm based on the Lagrange perspective that seeks the GNE. In addition, we provide a sufficient and necessary condition for the GNE of the considered problem.