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Financial markets and more generally macro-economic models involve a largenumber of individuals interacting through variables such as prices resultingfrom the aggregate behavior of all the agents. Mean field games have beenintroduced to study Nash equilibria for such problems in the limit when thenumber of players is infinite. The theory has been extensively developed in thepast decade, using both analytical and probabilistic tools, and a wide range ofapplications have been discovered, from economics to crowd motion. Morerecently the interaction with machine learning has attracted a growinginterest. This aspect is particularly relevant to solve very large games withcomplex structures, in high dimension or with common sources of randomness. Inthis chapter, we review the literature on the interplay between mean fieldgames and deep learning, with a focus on three families of methods. A specialemphasis is given to financial applications.

Deep Learning for Mean Field Games and Mean Field Control with Applications to Finance