Summary
Many engineering problems involve multiple decision-makers who must find a balance that suits everyone, called a generalized Nash equilibrium. Usually, these methods require all parties to share certain internal values, which can reduce privacy and increase communication. The authors developed a way for the parties to reach an equilibrium without sharing these internal values, which improves privacy and reduces communication needs. They also showed that their method reliably reaches a solution under certain conditions using a mathematical stability framework.
What this means in practice
- •For network schedulers: Implement distributed resource allocation schemes without exchanging sensitive multiplier information among nodes.
- •For energy grid operators: Coordinate distributed energy resources to reach equilibria while preserving local data privacy and reducing communication overhead.
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.