Fully Distributed Generalized Nash Equilibrium Seeking with Multiple Heterogeneous Players

This paper solves the fully distributed generalized Nash equilibrium (GNE) seeking problem of multiple heterogeneous players over undirected communication networks. Each player has a cost function that depends on the strategies of all players and is accessible only to the player itself. Moreover, the strategies of all players are coupled by a linear constraint set. Then, to reach the objective of GNE seeking problem, a fully distributed GNE seeking strategy is proposed by utilizing the output regulation technique, the adaptive parameter method and an augmented gradient-play dynamics. Unlike existing works that only consider simple dynamics and require the global information, 1) the heterogeneous dynamics are considered in this paper and the outputs of multiple heterogeneous players are driven to the GNE in a distributed fashion, and 2) the GNE seeking strategy does not require known information about the Lipschitz and monotone constants of the pseudo-gradient, as well as the algebraic connectivity of the graph. Finally, the effectiveness of the theoretical results is demonstrated.