##### 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.

##### Introduction to Decision Making and Uncertainty

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.

##### Distributed Solutions to Complex Societal Problems

###### Fall 2021 Long Program

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.

##### Decision Making and Uncertainty

###### Spring 2022 Long Program

Economics, finance, and business activities like marketing, operations management, and R&D all substantially rely on the use of formal, mathematical approaches to model human behavior, agents’ interaction, trading exchanges, mitigation of risks, and more. However, these areas are all rich enough that many important challenges are as yet unmet and new ones are constantly arising. For example, recent advances in data science, new platforms and means of human interaction, the growing speed of trading exchanges and flow of information, and various technological and other breakthroughs are all fertile ground motivating the use of new mathematical and statistical models and methods.

The mathematical sciences can play a crucial role by providing a platform on which to build and analyze innovative and complex models and as well as rigorous frameworks to solve the associated problems. However, this alone is not enough to make breakthrough progress. An intense scientific dialogue is needed so that the analysis of real-world problems may benefit from mathematical and statistical innovations, while, at the same time, the discipline and focus provided by such problems may help the mathematics from becoming remote from the real-world challenges. The intention of this program is to create and facilitate such an interdisciplinary dialogue by bringing together mathematicians, statisticians, economists, computer scientists, and researchers from operations research and business.