Control of McKean-Vlasov Dynamics (Mean Field Control) and the Price of Anarchy

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Rettaliata Engineering Center, Room 124
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Host

Department of Applied Mathematics

Speaker

René Carmona
Department of Operations Research and Financial Engineering, Princeton University
https://www.princeton.edu/~rcarmona/



Description

We posit a new form of the optimal control of stochastic differential equations of McKean-Vlasov type (often called Mean Field Control), and we derive the corresponding Pontryagin maximum principle. This requires calculus over the Wasserstein space of probability measures. We contrast the resulting optima with the Nash equilibria of the associated Mean Field Games (MFGs), and we investigate the price of anarchy by comparing the results of centralized optimization to those of decentralized optimization of MFGs.

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