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Mean-Field optimal control and other types of games

Massimo Fornasier, Techniche Universität München

In the first part of the course we introduce the concept of mean-field optimal control, which is the rigorous limit process connecting finite dimensional optimal control problems with ODE constraints modeling multi-agent interactions to an infinite dimensional optimal control problem with a constraint given by a PDE of Vlasov-type, governing the dynamics of the probability distribution of interacting agents.
In the second part of the course we introduce and study a mean-field model for a system of spatially distributed players interacting through an evolutionary game driven by a replicator dynamics. Strategies evolve by a replicator dynamics influenced by the position and the interaction between different players and return a feedback on the velocity field guiding their motion.

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Short Bio:

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Massimo Fornasier received his doctoral degree in computational mathematics in 2003 from the University of Padua, Italy. After spending from 2003 to 2006 as a postdoctoral research fellow at the University of Vienna and University of Rome La Sapienza, he joined the Johann Radon Institute for Computational and Applied Mathematics (RICAM) of the Austrian Academy of Sciences where he served as a senior research scientist until March 2011.

He was an associate researcher from 2006 to 2007 for the Program in Applied and Computational Mathematics of Princeton University, USA.

In 2011 Fornasier was appointed Chair of Applied Numerical Analysis at the Technical University of Munich.

The research of Massimo Fornasier embraces a broad spectrum of problems in mathematical modeling, analysis and numerical analysis.

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