Continuous-Time Distributed Seeking for Variational Generalized Nash Equilibrium of Online Game

TL;DR

This paper introduces two continuous-time distributed algorithms for seeking variational generalized Nash equilibria in online games, featuring constant regret bounds, reduced communication, noise resilience, and validated through UAV swarm and Nash-Cournot examples.

Contribution

The paper proposes novel continuous-time algorithms with event-triggered communication and noise resilience for VGNE seeking in online games, advancing distributed game theory methods.

Findings

Algorithms achieve constant regret and sublinear fit bounds.

Event-triggered mechanism reduces communication without losing performance.

Resilience to measurement noise is demonstrated in theoretical analysis.

Abstract

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.