Introduction to Mean Field Games and Applications
June 1-25, 2021
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.
Distributed Solutions to Complex Societal Problems
Fall 2021 Long Program
September 20-December 17, 2021
The need to understand and model large populations of rational agents interacting through intricate networks of connections is ubiquitous in modern science. Problems along these lines arise in settings such as the economy, global conflicts, and the spread of diseases, and they raise consequential regulatory issues. Population control, crowd analysis, smart cities, and self-driving vehicles present problems of a similar nature that are often tackled with tools from machine learning and artificial intelligence. However, in spite of spectacular successes, the lack of a deep understanding of how robots and human beings learn to navigate their environments and make forward looking decisions remains a major impediment to systematic progress, and the debate on the relative merits of centralized versus decentralized intelligence remains very much alive.
The theory of Mean Field Games (MFG) is an important mathematical framework that contributes to the understanding of such problems. It provides an approach to studying models in which a large number of agents interact strategically in a stochastically evolving environment, all responding to various shocks and incentives, and all trying to simultaneously forecast the decisions of others.
Introduction to Decision Making and Uncertainty
Jun 28-July 23, 2021
How do we make decisions in the face of risk? The need to make decisions in the presence of uncertainty cuts across a wide range of issues in science and human behavior. The underlying problems require both sophisticated modeling and advanced mathematical and statistical approaches and techniques.
This program will serve as an introduction to the long program on Decision Making and Uncertainty scheduled for Spring 2022. It aims to introduce participants to a variety of modeling questions and methods of current interest in this area. It will be built on “thematic clusters” of emerging areas of application.