Non-Normalized Solutions of Generalized Nash Equilibrium in Autonomous Racing
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912317061464064 |
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| author | Pustilnik, Mark Loquercio, Antonio Borrelli, Francesco |
| author_facet | Pustilnik, Mark Loquercio, Antonio Borrelli, Francesco |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12002 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Normalized Solutions of Generalized Nash Equilibrium in Autonomous Racing Pustilnik, Mark Loquercio, Antonio Borrelli, Francesco Robotics Computer Science and Game Theory Optimization and Control 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. |
| title | Non-Normalized Solutions of Generalized Nash Equilibrium in Autonomous Racing |
| topic | Robotics Computer Science and Game Theory Optimization and Control |
| url | https://arxiv.org/abs/2503.12002 |