Vector Cost Bimatrix Games with Applications to Autonomous Racing

2025/07/07 by Benjamin R. Toaz, Toaz, Benjamin R., Shaunak D. Bopardikar +1 · 1 citation
Computer Science · #Advanced Database Systems and Queries #Artificial Intelligence in Games #Computer Science and Game Theory (cs.GT) #Data Management and Algorithms #FOS: Computer and information sciences

paper · pdf · doi:10.48550/arxiv.2507.05171

openalex publication_date 2025/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We formulate a vector cost alternative to the scalarization method for weighting and combining multi-objective costs. The algorithm produces solutions to bimatrix games that are simultaneously pure, unique Nash equilibria and Pareto optimal with guarantees for avoiding worst case outcomes. We achieve this by enforcing exact potential game constraints to guide cost adjustments towards equilibrium, while minimizing the deviation from the original cost structure. The magnitude of this adjustment serves as a metric for differentiating between Pareto optimal solutions. We implement this approach in a racing competition between agents with heterogeneous cost structures, resulting in fewer collision incidents with a minimal decrease in performance. Code is available at https://github.com/toazbenj/race_simulation.

Citations

• α-RACER: Real-Time Algorithm for Game-Theoretic Motion Planning and Control in Autonomous Racing using Near-Potential Function
• Bridging the Gap between Discrete Agent Strategies in Game Theory and Continuous Motion Planning in Dynamic Environments
• Scalarizing Multi-Objective Robot Planning Problems using Weighted Maximization
• Adapting to Human Preferences to Lead or Follow in Human-Robot Collaboration: A System Evaluation
• Deep Latent Competition: Learning to Race Using Visual Control Policies in Latent Space
• Encoding Defensive Driving as a Dynamic Nash Game
• A Non-Cooperative Game Approach to Autonomous Racing
• A Unified Game-Theoretic Approach to Multiagent Reinforcement Learning

Cited by

• Vector Cost Behavioral Planning for Autonomous Robotic Systems with Contemporary Validation Strategies

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