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

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 …

In this paper, we deepen the analysis of continuous time Fictitious Play learning algorithm to
the consideration of various finite state Mean Field Game settings (finite horizon, $\gamma …

Non-cooperative and cooperative games with a very large number of players have many
applications but remain generally intractable when the number of players increases …

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 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 continues the study of the mean field game (MFG) convergence problem: In what
sense do the Nash equilibria of n-player stochastic differential games converge to the mean …

The mean field limit of large-population symmetric stochastic differential games is derived in
a general setting, with and without common noise, on a finite time horizon. Minimal …

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

We analyze a family of portfolio management problems under relative performance criteria,
for fund managers having CARA or CRRA utilities and trading in a common investment …