025w: Mean field games, mean field type control theory and applications


Sergey Kabanikhin, Institute of Computational Mathematics and Mathematical Geophysics of SB RAS

Vasily Kolokol'tsov, HSE

Yuri Averbukh, Krasovskii Institute of Mathematics and Mechanics of UB RAS


03 October 2022 - 07 October 2022


The purpose of the proposing workshop is to bring together the people studying the interaction of many intellectual agents. Such problems are formalized within the mean field game and mean field type control theory those examines the limiting systems consisting of infinitely many agents. The mean field type control problems arise when we assume that the agents behave collectively to achieve a common goal, whilst the systems with agents maximizing their own utility are subject of the mean field game theory. Despite of this difference, both theories have much in common. Their key object is a dynamical system in the space of probability measure. They involves the optimal control tools like Bellman equation and requires such objects as derivative (and more general subdifferentials) in the space of probability measures.

Notice that one can regard the mean field theories as a natural extension of the theory of McKean-Vlasov equations and more generally the theory of nonlinear Markov processes. The rapid  development of mean field games and the mean field type control theory was inspired by prominent works by Lasry, Lions (and, independently), Huang, Caines, Malhamé published in 2006. The actuality of this direction is testified by the enormous number of papers examining the mean field games and mean field type control systems, several books. Furthermore, the mean field games and mean field type control problems find various applications in economics, finance, power control, analysis of social interactions, including crime prevention, cybersecurity and opinion dynamics.