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 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 …

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 consider linear–quadratic mean field Stackelberg differential games with the adapted
open-loop information structure of the leader. There are one leader and N followers, where …

This paper considers two classes of large population stochastic differential games
connected to optimal and robust decentralized control of large-scale multiagent systems …

We construct a small time strong solution to a nonlocal Hamilton–Jacobi equation (1.1)
introduced in [48], the so-called master equation, originating from the theory of Mean Field …

This paper analyzes the problem of computing the social optimum in models with
heterogeneous agents subject to idiosyncratic shocks. This is equivalent to a deterministic …

In this paper, we consider discrete-time dynamic games of the mean-field type with a finite
number N of agents subject to an infinite-horizon discounted-cost optimality criterion. The …

We consider stochastic differential games with N players, linear-Gaussian dynamics in
arbitrary state-space dimension, and long-time-average cost with quadratic running cost …