A Data Driven Structural Decomposition of Dynamic Games via Best Response Maps
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arXiv
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| Format: | Preprint |
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2026
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| author | Rabbani, Mahdis Mojahed, Navid Nazari, Shima |
| author_facet | Rabbani, Mahdis Mojahed, Navid Nazari, Shima |
| contents | Dynamic games are powerful tools to model multi-agent decision-making, yet computing Nash (generalized Nash) equilibria remains a central challenge in such settings. Complexity arises from tightly coupled optimality conditions, nested optimization structures, and poor numerical conditioning. Existing game-theoretic solvers address these challenges by directly solving the joint game, typically requiring explicit modeling of all agents' objective functions and constraints, while learning-based approaches often decouple interaction through prediction or policy approximation, sacrificing equilibrium consistency. This paper introduces a conceptually novel formulation for dynamic games by restructuring the equilibrium computation. Rather than solving a fully coupled game or decoupling agents through prediction or policy approximation, a data-driven structural reduction of the game is proposed that removes nested optimization layers and derivative coupling by embedding an offline-compiled best-response map as a feasibility constraint. Under standard regularity conditions, when the best-response operator is exact, any converged solution of the reduced problem corresponds to a local open-loop Nash (GNE) equilibrium of the original game; with a learned surrogate, the solution is approximately equilibrium-consistent up to the best-response approximation error. The proposed formulation is supported by mathematical proofs, accompanying a large-scale Monte Carlo study in a two-player open-loop dynamic game motivated by the autonomous racing problem. Comparisons are made against state-of-the-art joint game solvers, and results are reported on solution quality, computational cost, and constraint satisfaction. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_05324 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Data Driven Structural Decomposition of Dynamic Games via Best Response Maps Rabbani, Mahdis Mojahed, Navid Nazari, Shima Computer Science and Game Theory Multiagent Systems Robotics Systems and Control Optimization and Control Dynamic games are powerful tools to model multi-agent decision-making, yet computing Nash (generalized Nash) equilibria remains a central challenge in such settings. Complexity arises from tightly coupled optimality conditions, nested optimization structures, and poor numerical conditioning. Existing game-theoretic solvers address these challenges by directly solving the joint game, typically requiring explicit modeling of all agents' objective functions and constraints, while learning-based approaches often decouple interaction through prediction or policy approximation, sacrificing equilibrium consistency. This paper introduces a conceptually novel formulation for dynamic games by restructuring the equilibrium computation. Rather than solving a fully coupled game or decoupling agents through prediction or policy approximation, a data-driven structural reduction of the game is proposed that removes nested optimization layers and derivative coupling by embedding an offline-compiled best-response map as a feasibility constraint. Under standard regularity conditions, when the best-response operator is exact, any converged solution of the reduced problem corresponds to a local open-loop Nash (GNE) equilibrium of the original game; with a learned surrogate, the solution is approximately equilibrium-consistent up to the best-response approximation error. The proposed formulation is supported by mathematical proofs, accompanying a large-scale Monte Carlo study in a two-player open-loop dynamic game motivated by the autonomous racing problem. Comparisons are made against state-of-the-art joint game solvers, and results are reported on solution quality, computational cost, and constraint satisfaction. |
| title | A Data Driven Structural Decomposition of Dynamic Games via Best Response Maps |
| topic | Computer Science and Game Theory Multiagent Systems Robotics Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2602.05324 |