Neural Mean-Field Games: Extending Mean-Field Game Theory with Neural Stochastic Differential Equations

Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of 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 introduce neural mean-field games: a combination of mean-field game theory and deep learning in the form of neural stochastic 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 two mean-field games that vary in their complexity, observability, and the presence of noise. Lastly, we illustrate the model's robustness by simulating viral dynamics based on real-world data. Here, we demonstrate that the model's ability to learn from real-world data helps to accurately model the evolution of an epidemic outbreak. Using these results, we show that the model is flexible, generalizable, and requires few observations to learn the distribution underlying the data.