**Distributed Solutions to Complex Societal Problems**

### Fall 2021 Long Program

### September 20-December 17, 2021

**Organizers**:

- Pierre Cardaliaguet (Mathematics, Paris-Dauphine)
- Annalisa Cesaroni (Statistics, Padova)
- Daniela Tonon (Mathematics, Paris-Dauphine)

- René Carmona (Operations Research and Financial Engineering, Princeton)
- Pierre-Louis Lions (Collège de France)
- Takis Souganidis (Mathematics, Chicago)

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. A short program Introduction to Mean Field Games and Applications will take place in June 2021 and serve as an introduction to this program.

The mathematical paradigm of MFG offers a powerful approach to the study of a number of challenging problems in social economics. It leads to a set of effective equations capturing the equilibrium behavior of large populations of interacting agents, often in situations which were believed to be intractable not so long ago. Many of the early successes of MFG were in engineering, but a second generation of applications will have broader impact and lead to better regulations, policies, and approaches to conflict resolution.

This program will bring to the fore mathematical advances in the theory and bring them to bear on applications where Mean Field Games can make a difference. It will facilitate an extensive interaction between mathematicians, statisticians, and applied scientists to advance the theory and better understand the applications.

The following workshops will be part of this program:

**Opening Workshop: An Introduction to the area of distributed solutions**

October 4-7, 2021

Organizers: Pierre Cardaliaguet (University of Paris-Dauphine and PSL) and Rene Carmona (ORFE, Princeton)

**Mean-field approaches in Machine Learning and Statistics**

October 18-21, 2021

Marc Hoffmann (University of Paris-Dauphine) and Francis Bach (INRIA and Ecole Normale Superieure)

**Aggregate dynamics in models with heterogeneous agents**

October 27-29

Organizer: Fernando Alvarez (University of Chicago Economics)

**Mean Field Models for interacting agents**

November 1-4, 2021

Organizers: Annalisa Cesaroni (Padova), Qiang Du (Columbia University), Benedetto Piccoli (Rutgers University), and Marie-Therese Wolfram (University of Warwick)

**Workshop on Applications of Mean Field Games: from Models to Practice**

November 16-19, 2021

Clemence Allasseur (Finance For Energy Market Research Centre EDF), Damien Fessler (University of Paris-Dauphine and PSL), and Mike Ludkovski (Statistics and Applied Probability, UC Santa Barbara)

**Applications to Financial Engineering**

December 6-8, 2021

Organizers: Rene Carmona (ORFE, Princeton) and Beatrice Acciaio (ETH-Zurich)

**Mathematical Advances in Mean Field Games**

December 13-17, 2021

Organizers: Long program organizing committee