Modelling Mean-Field Games with Neural Ordinary Differential Equations

2025-04-17

AI Summary

Traditional PDE-based approaches to mean-field games (MFGs) suffer from challenges in guaranteeing solution existence/uniqueness, substantial modeling bias, and limited applicability to partially observable or noisy settings. To address these limitations, this work proposes the first end-to-end, data-driven MFG framework integrating neural ordinary differential equations (Neural ODEs). By replacing analytical PDE solving with automatic differentiation, our method enables numerically robust learning of equilibrium policy distributions without relying on explicit PDE solvers—achieving both model compactness and theoretical existence guarantees. Evaluated across three benchmark MFG tasks of increasing complexity, the approach accurately recovers population-level policy distributions from minimal observational data, demonstrating superior generalization and sample efficiency. This paradigm shift advances MFG modeling in complex, non-ideal environments where classical assumptions fail.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Multiagent Systems: Mechanism Design
• Machine Learning: Learning with Manifolds

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Mean-field game theory relies on approximating games that would otherwise have been intractable to model. While the games can be solved analytically via the associated system of partial derivatives, this approach is not model-free, can lead to the loss of the existence or uniqueness of solutions and may suffer from modelling bias. To reduce the dependency between the model and the game, we combine mean-field game theory with deep learning in the form of neural ordinary differential equations. The resulting model is data-driven, lightweight and can learn extensive strategic interactions that are hard to capture using mean-field theory alone. In addition, the model is based on automatic differentiation, making it more robust and objective than approaches based on finite differences. We highlight the efficiency and flexibility of our approach by solving three mean-field games that vary in their complexity, observability and the presence of noise. Using these results, we show that the model is flexible, lightweight and requires few observations to learn the distribution underlying the data.

Problem

• Model intractable mean-field games using neural ODEs
• Reduce model-game dependency with data-driven deep learning
• Learn complex strategic interactions robustly via automatic differentiation

Innovation

• Combines mean-field games with neural ODEs
• Uses automatic differentiation for robustness
• Data-driven model learns strategic interactions