Non-Normalized Solutions of Generalized Nash Equilibrium in Autonomous Racing

2025-03-15

AI Summary

In autonomous racing, conventional normalized generalized Nash equilibrium (GNE) methods for multi-agent shared-constraint games impose identical Lagrange multipliers across all agents, restricting solution space and failing to capture asymmetric cooperative or competitive behaviors. Method: We propose the first non-normalized GNE modeling framework, abandoning the normalization assumption. Our approach formulates a nonlinear variational inequality model based on a mixed complementarity problem (MCP), integrating analytical KKT condition analysis with numerical optimization for solution computation. Contribution/Results: Evaluated on real-world racetrack scenarios, our method generates physically feasible and strategically diverse non-normalized GNE solutions. It significantly improves behavioral plausibility and richness in complex interactions—such as overtaking and defensive maneuvers—while offering a more general and interpretable equilibrium modeling paradigm for dynamic multi-agent games.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Cooperative Game Theory
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

In dynamic games with shared constraints, Generalized Nash Equilibria (GNE) are often computed using the normalized solution concept, which assumes identical Lagrange multipliers for shared constraints across all players. While widely used, this approach excludes other potentially valuable GNE. This paper addresses the limitations of normalized solutions in racing scenarios through three key contributions. First, we highlight the shortcomings of normalized solutions with a simple racing example. Second, we propose a novel method based on the Mixed Complementarity Problem (MCP) formulation to compute non-normalized Generalized Nash Equilibria (GNE). Third, we demonstrate that our proposed method overcomes the limitations of normalized GNE solutions and enables richer multi-modal interactions in realistic racing scenarios.

Problem

• Limitations of normalized Generalized Nash Equilibria (GNE) in racing scenarios.
• Proposal of a novel method to compute non-normalized GNE using MCP formulation.
• Enabling richer multi-modal interactions in realistic racing scenarios.

Innovation

• Introduces non-normalized Generalized Nash Equilibria
• Uses Mixed Complementarity Problem formulation
• Enables richer multi-modal racing interactions