Open Doctoral Lectures - Numerical methods for mean field games - 06/07/2023

Mean field games have been introduced to study very large populations of strategic agents interacting in a symmetric way. The theoretical foundation has been extensively developed, and potential applications have been proposed in a wide range of fields, from economics to sociology and engineering. Applying mean field games to real-world problems requires efficient computational methods. In this course, we will review existing methods. After introducing the mean field game framework, we will discuss methods based on classical tools such as finite difference schemes. These methods are well understood from the numerical analysis viewpoint, and they are very efficient, when they can be applied. We will then present recent methods relying on deep learning, which can be used for high dimensional problems. Last, we will discuss model-free reinforcement learning methods. During this course, numerical illustrations and samples of codes will be presented.