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Workshop: Mean-field games - April 10-17, 2022

MFG theory lies at the intersection of probability and partial differential equations (PDEs). On the one hand, MFG models raise interesting new probabilistic questions about how stochastic optimal control and game-theoretic equilibria interact with classical limit theorems; for example, even if players are influenced only by their own independent random factors, a game-theoretic interaction between players can induce a dependence between their resulting behaviours, which precludes a direct application of the law of large numbers or central limit theorem. On the other hand, the study of MFGs leads to novel PDE systems, the most famous of which is a forward-backward system coupling a Hamilton-Jacobi-Bellman equation, de- scribing the value function of a typical player, with a Fokker-Planck equation, describing the distribution of players' behaviours.