Fully Distributed GNE Algorithms for Multi-Robot Placement without Consensus on Multipliers

Abstract:Recent machine learning research has increasingly focused on equilibrium analysis in non-cooperative games rather than solely on optimal solutions. Many such problems involve shared constraints and can be formulated as Generalized Nash Equilibrium Problems (GNEPs). For strongly monotone games, existing methods compute consensus-based variational GNEs (v-GNEs) by exchanging Lagrange multipliers. We propose a fully distributed continuous-time algorithm for shared linear equality constraints that converges without multiplier exchange and reaches any GNE, reducing communication overhead and improving privacy. Discrete-time schemes are also provided, and the method is validated on a multi-robot placement task.

6 pages, 3 figures. Published in the 2026 American Control Conference (ACC), pp. 3633--3638

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computer Science and Game Theory (cs.GT); Multiagent Systems (cs.MA); Robotics (cs.RO)

arXiv:2608.29388 [cs.LG]

(or arXiv:2608.29388v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2608.29388 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

2026 American Control Conference (ACC), pp. 3633--3638, 2026

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