Modelling Mean-Field Games with Neural Ordinary Differential Equations

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.