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 …

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 …

In this paper we formulate and analyze an N-player stochastic game of the classical fuel
follower problem and its mean field game (MFG) counterpart. For the N-player game, we …

In this paper, we study the backward stochastic differential equation (BSDE) with two
nonlinear mean reflections, which means that the constraints are imposed on the distribution …

Given a domain G, a reflection vector field d(⋅) on ∂G, the boundary of G, and drift and
dispersion coefficients b(⋅) and σ(⋅), let L be the usual second-order elliptic operator …

This article studies singular mean field control problems and singular mean field two-players
stochastic differential games. Both sufficient and necessary conditions for the optimal …

We introduce a non-zero-sum game between a government and a legislative body to study
the optimal level of debt. Each player, with different time preferences, can intervene on the …

A multiclass many-server system is considered, in which customers are served according to
a nonpreemptive priority policy and may renege while waiting to enter service. The service …

The deterministic Skorohod problem plays an important role in the construction and analysis
of diffusion processes with reflection. In the form studied here, the multidimensional …

We study a continuous-time, finite horizon, stochastic partially reversible investment problem
for a firm producing a single good in a market with frictions. The production capacity is …