Generalized Nash Equilibrium Seeking via Continuous-Time Coordination Dynamics Over Digraphs

This article studies a generalized Nash equilibrium problem with coupling equality constraints and local action sets, where the cost function of each player has a general form that depends on the actions of other players in this game. In the case that the players cannot directly use the others' actions, all players are allowed to estimate their opponents' actions by communicating with their neighbors over a digraph. In this regard, continuous-time coordination dynamics are proposed for two kinds of directed communication topologies including weight-balanced and weight-unbalanced digraphs. When the pseudogradient is strongly monotone and Lipschitz continuous as well as the extended pseudogradient is Lipschitz continuous, it is theoretically shown that the proposed dynamics could solve the generalized Nash equilibrium problem with and without local action sets, respectively. Finally, the obtained theoretical results are illustrated by numerical simulations.