Introduction to Mean Field Games and Applications

This program provides mathematical background for the long program in Fall 2021 on Distributed Solutions to Complex Societal Problems. Examples of the problems to be addressed in the long program include modeling phenomena such as the macroeconomy, conflict, financial regulation, crowd movement, big data, and advertising, as well as engineering problems involving decentralized intelligence, machine learning, and telecommunications.

An important mathematical development contributing to the understanding of such problems is the theory of Mean Field Games. This is a mathematical framework well-suited to the study of models in which a large number of agents interact strategically in a stochastically evolving environment, all responding to a range of incentives, and all trying to simultaneously forecast the decisions of other agents.

The tutorial lectures will be complemented by discussions and short talks on related topics.

The intended audience consists of advanced graduate students, postdocs, and researchers interested in the general topic who have some knowledge of probability, stochastic analysis, and partial differential equations. If necessary, some of the more advanced background material will be presented in additional lectures.

Material from the first two weeks is a prerequisite for the rest of the program. Attendees who are not familiar with that material are encouraged to participate in the entire program.

The program will consist of the following six tutorials.