We force uniqueness in finite state mean field games by adding a Wright–Fisher common
noise. We achieve this by analyzing the master equation of this game, which is a degenerate …

The purpose of this work is to introduce a notion of weak solution to the master equation of a
potential mean field game and to prove that existence and uniqueness hold under quite …

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 …

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 …

We present the notion of monotone solution of mean field games master equations in the
case of a continuous state space. We establish the existence, uniqueness and stability of …

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 …

In an extended mean field game the vector field governing the flow of the population can be
different from that of the individual player at some mean field equilibrium. This new class …

We examine mean field control problems on a finite state space, in continuous time and over
a finite time horizon. We characterize the value function of the mean field control problem as …

The goal of this paper is to demonstrate that common noise may serve as an exploration
noise for learning the solution of a mean field game. This concept is here exemplified …

In this paper, we study a class of linear-quadratic (LQ) mean field games of controls with
common noises and their corresponding $ N $-player games. The theory of mean field game …