In this manuscript we propose a structural condition on nonseparable Hamiltonians, which
we term displacement monotonicity condition, to study second-order mean field games …

This paper studies the convergence problem for mean field games with common noise. We
define a suitable notion of weak mean field equilibria, which we prove captures all …

It is well known that the monotonicity condition, either in Lasry–Lions sense or in
displacement sense, is crucial for the global well-posedness of mean field game master …

We present a new notion of solution for mean field games master equations. This notion
allows us to work with solutions which are merely continuous. We first prove results of …

In this paper we study second order master equations arising from mean field games with
common noise over arbitrary time duration. A classical solution typically requires the …

In the presence of a common noise, we study the convergence problems in mean field game
(MFG) and mean field control (MFC) problem where the cost function and the state dynamics …

We provide an abstract framework for submodular mean field games and identify verifiable
sufficient conditions that allow us to prove the existence and approximation of strong mean …

In this paper, we study graphon mean field games using a system of forward–backward
stochastic differential equations. We establish the existence and uniqueness of solutions …

Forcing finite state mean field games by a relevant form of common noise is a subtle issue,
which has been addressed only recently. Among others, one possible way is to subject the …

The goal of this paper is to provide a selection principle for potential mean field games on a
finite state space and, in this respect, to show that equilibria that do not minimize the …