Description

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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 summer school on Introduction to Mean Field Games and Applications during June 2021 will 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.

Organizers

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P C
Pierre Cardaliaguet Mathematics, Université Paris-Dauphine and PSL
R C
René Carmona Operations Research and Financial Engineering, Princeton University
A C
Annalisa Cesaroni Statistics, Università di Padova
P L
Pierre-Louis Lions Collège de France
D T
Daniela Tonon Dipatimento di Matematica, Universita degli Studi di Padova
T S
Takis Souganidis Mathematics, University of Chicago

Program Workshops

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Workshop
Introduction to Distributed Solutions
expanded

This conference will consist of three series of lectures, the aim of which is to present the main issues at stake in the analysis of distributed solutions to complex societal problems and to describe some mathematical tools to handle these questions. Applications range from collective behavior in economy and finance to crowd analysis and the spread of diseases, and from machine learning to stochastic optimization and artificial intelligence.

Workshop
Short Courses on the Mean Field Approach in Machine Learning and Statistics
expanded

This online workshop will consist of three series of lectures discussing aspects of the Mean Field approach in machine learning and statistics.

Workshop
Aggregate Dynamics in Models with Heterogeneous Agents
expanded

This conference invites participants to present and discuss current research on models with the following features. The heterogeneous agents feature refers to agents solving dynamic problems subject to idiosyncratic random shocks, each agent with non-trivial interactions with the remaining agents. The “aggregate dynamics” feature refers to the focus on the understanding and characterization of the dynamics of the entire system, either itself subject to aggregate shock or as a deterministic system, using analytical or numerical techniques. Examples of such models are variants of Mean Field Games. Models will have applications in several fields in economics and intersections with other disciplines.

Workshop
Mean-Field Models for Interacting Agents
expanded

Interacting particle models are a powerful mathematical tool to model the behavior of large groups in economics as well as in the life and social sciences. Understanding the dynamics of these systems on different levels is of great importance, as it gives insights into the emergence of many complex phenomena. In this workshop we will focus on recent developments and emerging challenges in the derivation and analysis of these micro- and mean-field models. It will feature different perspectives and approaches to these challenges, by bringing together applied mathematicians working at the interfaces between statistics, social sciences and the life sciences.

Workshop
Applications of Mean Field Games
expanded

The paradigm of Mean Field Games (MFG) has become a major connection between distributed decision-making and stochastic modeling. Starting out in the stochastic control literature, it is gaining rapid adoption across a range of industries. The objective of this workshop is to give a clear vision of how MFG tools are being used in practical settings, both in complement and in contrast to the usual methodologies. The workshop will gather researchers both from industry and universities and will focus on diverse application areas.

Workshop
Applications to Financial Engineering
expanded

Mean field theories, Mean Field Games, and Mean Field Control are theoretical concepts which can naturally be brought to bear in applications to financial engineering. The workshop will examine how they influenced the development of financial mathematics theoretical works and the implementation of financial engineering solutions to problems involving large ensembles of individuals or robots optimizing their behaviors in uncertain and complex environments.

Workshop
Mathematical Advances in Mean Field Games
expanded

Complex societal problems can be studied and modeled through the mathematical theory of Mean Field Games. Indeed MFGs are a mathematical modeling approach to stochastically evolving systems which involve a large number of indistinguishable rational agents that have the same optimization criteria. The theory of MFG is very lively and productive at the moment and several important results have been achieved that can be applied to engineering, economics, finance, social sciences, In this final workshop we present recent analytic, probabilistic and numerical advances in this theory.