A Data Driven Structural Decomposition of Dynamic Games via Best Response Maps

• URL: http://arxiv.org/abs/2602.05324v1
• Date: Thu, 05 Feb 2026 05:44:53 GMT
• Title: A Data Driven Structural Decomposition of Dynamic Games via Best Response Maps
• Abstract summary: This paper introduces a conceptually novel formulation for dynamic games by restructuring the equilibrium computation.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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