Following the remarkable success of the AlphaGO series, 2019 was a booming year that
witnessed significant advances in multi-agent reinforcement learning (MARL) techniques …

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 …

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 …

The purpose of this paper is to provide a complete probabilistic analysis of a large class of
stochastic differential games with mean field interactions. We implement the Mean-Field …

In this paper, we consider a mean-field stochastic differential equation, also called the
McKean–Vlasov equation, with initial data (t,x)∈0,T*R^d, whose coefficients depend on …

Mean Field Games (MFG) have been introduced to tackle games with a large number of
competing players. Considering the limit when the number of players is infinite, Nash …

This book grew out of the lecture notes I prepared for a graduate class I taught at Princeton
University in 2011–12, and again in 2012–13. My goal was to introduce the students to …

We analyze a class of nonlinear partial differential equations (PDEs) defined on $\mathbb
{R}^ d\times\mathcal {P} _2 (\mathbb {R}^ d), $ where $\mathcal {P} _2 (\mathbb {R}^ d) $ is …

We study optimal control of the general stochastic McKean--Vlasov equation. Such a
problem is motivated originally from the asymptotic formulation of cooperative equilibrium for …

This paper rigorously connects the problem of optimal control of McKean--Vlasov dynamics
with large systems of interacting controlled state processes. Precisely, the empirical …