Distributed event-triggered generalized Nash equilibrium seeking in multi-coalition noncooperative games with coupling constraints

This paper is concerned with a multi-coalition noncooperative game with coupling equality constraints. Each coalition is a player consisted of multiple agents in noncooperative games and desire to minimize its own objective function based on local information. Each agent as actual decision maker in the same coalition is to optimize the objective function of the coalition cooperately. To seek a generalized Nash equilibrium (GNE) of the multi-coalition game, a distributed continuous-time algorithm is developed. Moreover, to further reduce the communication among agents and coalitions, an event-triggered mechanism (ETM) is introduced for the multi-coalition game. By using ETM, a novel distributed GNE seeking algorithm is proposed, where agents and coalitions are allowed to exchange estimation information with neighbors only when the triggering condition is satisfied. Remarkably, the proposed event-triggered scheme introduces internal variables to regulate its threshold dynamically, which excludes Zeno behavior. By Lyapunov analysis, it is proved that the coalitions' decision variables converge to a GNE in both algorithms. Finally, the effectiveness of the proposed methods is validated by numerical simulations.