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On the systems of PDE in mean field games theory
Prof. Alessio Porretta, University of Rome Tor Vergata
Sala conferenze IMATI-CNR - Martedì 2 Febbraio 2016 h.15:00
Abstract. Mean field games theory was introduced by J-M. Lasry and P.-L. Lions as a model for describing strategic interactions in the dynamics of populations of several identical agents whenever the individual optimization criteria depend on the collective behavior. A mean field approach leads to a macroscopic model where Nash equilibria are interpreted as solutions of a system of PDEs, in which a backward Bellman equation for the individual strategy is strongly coupled with a forward Fokker-Planck equation for the mass distribution law. I will describe several features of those coupled systems, which bring new PDE issues as well as new connections with optimal control and transport problems.
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