Vector Cost Bimatrix Games with Applications to Autonomous Racing Article Swipe

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Benjamin R. Toaz , Shaunak D. Bopardikar ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2507.05171

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.

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2507.05171
PDF: https://arxiv.org/pdf/2507.05171
OA Status: green
OpenAlex ID: https://openalex.org/W4414687842

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DOI: https://doi.org/10.48550/arxiv.2507.05171

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Title: Vector Cost Bimatrix Games with Applications to Autonomous Racing

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Type: preprint

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Language: en

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Publication year: 2025

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Publication date: 2025-07-07

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Authors: Benjamin R. Toaz, Shaunak D. Bopardikar

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Landing page: https://arxiv.org/abs/2507.05171

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PDF URL: https://arxiv.org/pdf/2507.05171

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Cited by: 0

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