The mean-field framework was developed to study systems with an infinite number of
rational agents in competition, which arise naturally in many applications. The systematic …

This paper serves as an introduction and overview of the potentially useful models and
methodologies from artificial intelligence (AI) into the field of transportation engineering for …

The lion's share of this chapter is devoted to the construction of equilibria for mean field
games with a common noise. We develop a general two-step strategy for the search of weak …

Conic optimization is a significant and thriving research area within the optimization
community. Conic optimization is the general class of problems concerned with optimizing a …

This text is inspired from a “Cours Bachelier” held in January 2009 and taught by Jean-
Michel Lasry. This course was based upon the articles of the three authors and upon …

This survey paper presents some new advances in theoretical aspects of differential game
theory. We particular focus on three topics: differential games with state constraints; …

Mean field game theory is devoted to the analysis of differential games with a (very) larger
number of “small” players. By “small” player, we mean a player who has very little influence …

Mean field type models describing the limiting behavior, as the number of players tends to
+∞, of stochastic differential game problems, have been recently introduced by J.-M. Lasry …

This book brings together several recent developments on the regularity theory for mean-
field game systems. We detail several classes of methods and present a concise overview of …

We provide a comprehensive study of a general class of linear-quadratic mean field games.
We adopt the adjoint equation approach to investigate the unique existence of their …