Continuous-Time Distributed Seeking for Variational Generalized Nash Equilibrium of Online Game
This work addresses online noncooperative and aggregative games with constraints, offering incremental improvements in distributed algorithms for multi-agent systems.
The paper tackles distributed seeking of Variational Generalized Nash Equilibrium in online games with time-varying constraints, proposing continuous-time algorithms that achieve constant regret and sublinear fit bounds, and demonstrating noise resilience in applications like UAV swarms.
This paper mainly investigates a class of distributed Variational Generalized Nash Equilibrium (VGNE) seeking problems for both online noncooperative games and online aggregative games with time-varying coupling inequality constraints. Two novel continuous-time distributed VGNE seeking algorithms are proposed, which realize the constant regret bound and sublinear fit bound, superior to those of the criteria for online optimization problems and online games. Furthermore, to reduce unnecessary communication among players, a dynamic event-triggered mechanism involving internal variables is introduced into the distributed VGNE seeking algorithm, while the constant regret bound and sublinear fit bound are still maintained. Also, the Zeno behavior is strictly prohibited. Moreover, we further investigate the impact of communication noise on the player's measurement of its neighbors' relative states. It is demonstrated that both the regret and fit bounds remain valid as long as the noise level is not excessively large. This result reveals, to some extent, the proposed algorithm's noise-resilient capability. Finally, an online Uncrewed Aerial Vehicle (UAV) swarm game and an online Nash-Cournot game are given to demonstrate the validity of the theoretical results.