This book describes the latest advances in the theory of mean field games, which are
optimal control problems with a continuum of players, each of them interacting with the …

Mean field theory has raised a lot of interest in recent years, since the independent
introduction by Lasry–Lions and Huang–Caines–Malhamé, see, in particular, Lasry–Lions …

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 …

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 …

We consider the control of the COVID-19 pandemic through a standard SIR compartmental
model. This control is induced by the aggregation of individuals' decisions to limit their social …

This paper studies large population dynamic games involving nonlinear stochastic
dynamical systems with agents of the following mixed types:(i) a major agent and (ii) a …

We study the McKean–Vlasov optimal control problem with common noise which allow the
law of the control process to appear in the state dynamics under various formulations: strong …

We consider N-person differential games involving linear systems affected by white noise,
running cost quadratic in the control and in the displacement of the state from a reference …

The theory of mean field games (MFGs) studies the limiting behaviors of large systems
where the agents interact with each other in a certain symmetric way. The running and …