PDO-Split: A Real-Time Solver for Constrained Potential-Dominant Games

2026-09-25

AI Summary

This study addresses the computational bottleneck in solving multi-agent equilibria within game-theoretic model predictive control, which hinders real-time applicability. To overcome this challenge, we introduce the class of γ-potential-dominant games and propose a real-time generalized Nash equilibrium solver tailored to this structure. The algorithm integrates operator splitting with Karush–Kuhn–Tucker (KKT) system resolution, accelerating convergence through potential-component preconditioning while enhancing linear solve efficiency via LDL^T factorization reuse and symmetry exploitation. Experimental evaluations demonstrate that the proposed method significantly outperforms existing approaches in scenarios such as multi-vehicle racing. Furthermore, its real-time deployability is successfully validated on a micro-scale autonomous racing platform.

Abstract

We present Potential-Dominant Operator Splitting (PDO-Split), a real-time generalized Nash equilibrium solver for constrained dynamic multi-agent problems with potential-dominant structure. PDO-Split targets the computational bottleneck in game-theoretic model predictive control, where repeatedly solving the equilibrium KKT system becomes costly as the number of agents increases. We introduce a class of gamma-potential-dominant games, in which the potential (or cooperative) structure dominates the competitive interactions between the agents. We show that this structure allows PDO-Split to use the potential component as a preconditioner while incorporating the competitive component through iterative refinement. We establish convergence guarantees and exploit the symmetry of the potential component through a reusable LDL^T factorization to accelerate the linear solvers. We evaluate PDO-Split across several practical multi-agent planning problems, including eight-car racing and six-vehicle ramp merging, achieving substantially improved runtime and convergence rate over existing DDP-based and Newton-based methods, especially with a larger number of agents. The algorithm is also experimentally validated on miniature autonomous race car platforms, demonstrating the approach's real-time capability.

Problem

• Generalized Nash Equilibrium
• Game-Theoretic MPC
• Multi-Agent Systems
• Computational Bottleneck
• Potential-Dominant Games

Innovation

• Operator Splitting
• Generalized Nash Equilibrium
• Potential-Dominant Games
• Model Predictive Control
• LDL^T Factorization