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

2026-02-05

AI Summary

Computing Nash (or generalized Nash) equilibria in dynamic games is highly challenging due to coupled optimality conditions, nested optimization structures, and numerical ill-conditioning. This work proposes a data-driven, structured decomposition approach that circumvents these difficulties by offline construction of each agent’s best-response mapping, which is then embedded as a feasibility constraint. This formulation eliminates nested optimization and derivative coupling while preserving equilibrium consistency—without requiring explicit modeling of all objectives and constraints or approximation via policy prediction. By integrating best-response embedding, structured optimization reformulation, and large-scale Monte Carlo validation, the method significantly improves computational efficiency and constraint satisfaction in a two-player open-loop autonomous racing game, yielding high-quality approximate equilibrium solutions.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Equilibrium

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Dynamic games
• Nash equilibrium
• Generalized Nash equilibrium
• Equilibrium computation
• Multi-agent decision-making

Innovation

• best-response map
• structural decomposition
• data-driven equilibrium computation
• dynamic games
• Nash equilibrium