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Optimal transport, mean field games and gradient flows

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Systemic Risk: Mathematical Modelling and Interdisciplinary Approaches

I will review how optimal transport can be seen as a mean field game via the Benamou-Brenier formula. Then I will show how Nash-Cournot equilibria are related to local minimizers of interaction energies or free energies penalized with the Wassertein distance. I will discuss briefly numerical schemes based on the optimal transportation viewpoint for the evolution PDEs obtained which are related to gradient flows of the free energy.

This talk is part of the Isaac Newton Institute Seminar Series series.

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