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

arXiv: https://arxiv.org/abs/2608.29388 · HTML: https://mlsanity.com/paper/2608.29388/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 30 references that are in the map.
- First posted on arXiv 29 Aug 2026.

## Builds on (most cited first, 9 of 9)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Hyperparameter optimization with approximate gradient](https://mlsanity.com/paper/1602.02355/) (2016)
- [Mean Field Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1802.05438/) (2018)
- [Turbocharging Solution Concepts: Solving NEs, CEs and CCEs with Neural Equilibrium Solvers](https://mlsanity.com/paper/2210.09257/) (2022)
- [Convex-Concave Min-Max Stackelberg Games](https://mlsanity.com/paper/2110.05192/) (2021)
- [Asymptotic convergence of constrained primal-dual dynamics](https://mlsanity.com/paper/1510.02150/) (2015)
- [Augmented Lagrangian Methods for the Solution of Generalized Nash Equilibrium Problems](https://mlsanity.com/paper/1807.04474/) (2018)
- [Continuous-time fully distributed generalized Nash equilibrium seeking for multi-integrator agents](https://mlsanity.com/paper/1911.12266/) (2019)
- [An asynchronous distributed and scalable generalized Nash equilibrium seeking algorithm for strongly monotone games](https://mlsanity.com/paper/2005.03507/) (2020)

## Built on by (most cited first, 1 of 1)

- [Input-to-State Stability Framework for Fully Distributed Primal-Dual Dynamics for Quadratic GNEPs Without Multiplier Consensus](https://mlsanity.com/paper/2609.06983/) (2026)

## Abstract (arXiv)

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.