[图书][B] The master equation and the convergence problem in mean field games:(ams-201)
P Cardaliaguet, F Delarue, JM Lasry, PL Lions - 2019 - books.google.com
This book describes the latest advances in the theory of mean field games, which are
optimal control problems with a continuum of players, each of them interacting with the …
optimal control problems with a continuum of players, each of them interacting with the …
[图书][B] Probabilistic theory of mean field games with applications I-II
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 …
games with a common noise. We develop a general two-step strategy for the search of weak …
A machine learning framework for solving high-dimensional mean field game and mean field control problems
Mean field games (MFG) and mean field control (MFC) are critical classes of multiagent
models for the efficient analysis of massive populations of interacting agents. Their areas of …
models for the efficient analysis of massive populations of interacting agents. Their areas of …
Mean field games
PE Caines - Encyclopedia of systems and control, 2021 - Springer
The notion of the infinite population limit of large population games where agents are
realized by controlled stochastic dynamical systems is introduced. The theory of infinite …
realized by controlled stochastic dynamical systems is introduced. The theory of infinite …
Stochastic optimal control in infinite dimension
The main objective of this book is to give an overview of the theory of Hamilton–Jacobi–
Bellman (HJB) partial differential equations (PDEs) in infinite-dimensional Hilbert spaces …
Bellman (HJB) partial differential equations (PDEs) in infinite-dimensional Hilbert spaces …
[图书][B] Regularity theory for mean-field game systems
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 …
field game systems. We detail several classes of methods and present a concise overview of …
[图书][B] A probabilistic approach to classical solutions of the master equation for large population equilibria
We analyze a class of nonlinear partial differential equations (PDEs) defined on $\mathbb
{R}^ d\times\mathcal {P} _2 (\mathbb {R}^ d), $ where $\mathcal {P} _2 (\mathbb {R}^ d) $ is …
{R}^ d\times\mathcal {P} _2 (\mathbb {R}^ d), $ where $\mathcal {P} _2 (\mathbb {R}^ d) $ is …
On the convergence of closed-loop Nash equilibria to the mean field game limit
D Lacker - The Annals of Applied Probability, 2020 - JSTOR
This paper continues the study of the mean field game (MFG) convergence problem: In what
sense do the Nash equilibria of n-player stochastic differential games converge to the mean …
sense do the Nash equilibria of n-player stochastic differential games converge to the mean …
An introduction to mean field game theory
These notes are an introduction to Mean Field Game (MFG) theory, which models differential
games involving infinitely many interacting players. We focus here on the Partial Differential …
games involving infinitely many interacting players. We focus here on the Partial Differential …
From the master equation to mean field game limit theory: a central limit theorem
Mean field games (MFGs) describe the limit, as n tends to infinity, of stochastic differential
games with n players interacting with one another through their common empirical …
games with n players interacting with one another through their common empirical …