Summary
Some engineering problems involve many agents making decisions together, called Generalized Nash Equilibrium Problems (GNEPs). Most existing methods make the agents share certain information, called multipliers, which can increase communication and lower privacy. This paper presents a method where agents do not share multipliers, reducing communication and improving privacy. The authors prove their approach works well under certain conditions by using a stability analysis called input-to-state stability.
Generalized Nash Equilibrium Problemmulti-agent systemsdistributed algorithmsprimal-dual dynamicsmultiplier consensusinput-to-state stabilityconvergenceprivacyquadratic optimization
Abstract
Generalized Nash Equilibrium Problems (GNEPs) often arise in multi-agent engineering applications that require distributed algorithms. Unlike traditional approaches that enforce consensus on multipliers, our method removes the need to share multipliers, reducing communication and improving privacy. As a result, different initializations can lead to different GNEs, including non-variational ones. We establish convergence under sufficient conditions using an input-to-state stability (ISS) framework.