Finite state mean field games with Wright–Fisher common noise
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 …
noise. We achieve this by analyzing the master equation of this game, which is a degenerate …
Weak solutions to the master equation of potential mean field games
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 …
potential mean field game and to prove that existence and uniqueness hold under quite …
Mean field game master equations with anti-monotonicity conditions
C Mou, J Zhang - Journal of the European Mathematical Society, 2024 - ems.press
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 …
displacement sense, is crucial for the global well-posedness of mean field game master …
Wellposedness of second order master equations for mean field games with nonsmooth data
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 …
common noise over arbitrary time duration. A classical solution typically requires the …
Monotone solutions for mean field games master equations: continuous state space and common noise
C Bertucci - Communications in Partial Differential Equations, 2023 - Taylor & Francis
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 …
case of a continuous state space. We establish the existence, uniqueness and stability of …
Finite State Mean Field Games with Wright–Fisher Common Noise as Limits of N-Player Weighted Games
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 …
which has been addressed only recently. Among others, one possible way is to subject the …
Minimal solutions of master equations for extended mean field games
C Mou, J Zhang - Journal de Mathématiques Pures et Appliquées, 2024 - Elsevier
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 …
different from that of the individual player at some mean field equilibrium. This new class …
Finite state N-agent and mean field control problems
A Cecchin - ESAIM: Control, Optimisation and Calculus of …, 2021 - esaim-cocv.org
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 …
a finite time horizon. We characterize the value function of the mean field control problem as …
Exploration noise for learning linear-quadratic mean field games
F Delarue, A Vasileiadis - Mathematics of Operations …, 2024 - pubsonline.informs.org
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 …
noise for learning the solution of a mean field game. This concept is here exemplified …
Linear-quadratic mean field games of controls with non-monotone data
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 …
common noises and their corresponding $ N $-player games. The theory of mean field game …