𝔖 Scriptorium
✦   LIBER   ✦
📁

Regularity Theory for Mean-Field Game Systems

✍ Scribed by Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan (auth.)

Publisher
Springer International Publishing
Year
2016
Tongue
English
Leaves
165
Series
SpringerBriefs in Mathematics
Edition
1
Category
Library
⬇  Acquire This Volume

No coin nor oath required. For personal study only.

✦ Synopsis

Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.

✦ Table of Contents

Front Matter....Pages i-xiv
Introduction....Pages 1-8
Explicit Solutions, Special Transformations, and Further Examples....Pages 9-14
Estimates for the Hamilton–Jacobi Equation....Pages 15-37
Estimates for the Transport and Fokker–Planck Equations....Pages 39-61
The Nonlinear Adjoint Method....Pages 63-76
Estimates for MFGs....Pages 77-95
A Priori Bounds for Stationary Models....Pages 97-103
A Priori Bounds for Time-Dependent Models....Pages 105-109
A Priori Bounds for Models with Singularities....Pages 111-123
Non-local Mean-Field Games: Existence....Pages 125-130
Local Mean-Field Games: Existence....Pages 131-144
Back Matter....Pages 145-156

✦ Subjects

Game Theory, Economics, Social and Behav. Sciences;Economic Theory/Quantitative Economics/Mathematical Methods;Systems Theory, Control

📜 SIMILAR VOLUMES

Mean Field Games and Mean Field Type Con
📁 Mean Field Games and Mean Field Type Control Theory
✍ Alain Bensoussan, Jens Frehse, Phillip Yam (auth.) 📂 Library 📅 2013 🏛 Springer-Verlag New York 🌐 English

<p>​Mean field games and Mean field type control introduce new problems in Control Theory. The terminology “games” may be confusing. In fact they are control problems, in the sense that one is interested in a single decision maker, whom we can call the representative agent. However, these problems a

Regularity theory for mean curvature flo
📁 Regularity theory for mean curvature flow
✍ Klaus Ecker 📂 Library 📅 2004 🏛 Birkhäuser Boston 🌐 English

<P>This work is devoted to the motion of surfaces for which the normal velocity at every point is given by the mean curvature at that point; this geometric heat flow process is called mean curvature flow.</P> <P></P> <P>Mean curvature flow and related geometric evolution equations are important tool

Regularity theory for mean curvature flo
📁 Regularity theory for mean curvature flow
✍ Klaus Ecker 📂 Library 📅 2004 🏛 Birkhäuser 🌐 English

* Devoted to the motion of surfaces for which the normal velocity at every point is given by the mean curvature at that point; this geometric heat flow process is called mean curvature flow. * Mean curvature flow and related geometric evolution equations are important tools in mathematics and mat

Regularity Theory for Mean Curvature Flo
📁 Regularity Theory for Mean Curvature Flow
✍ Klaus Ecker (auth.) 📂 Library 📅 2004 🏛 Birkhäuser Basel 🌐 English

<p><P>"The central theme [in this book] is the regularity theory for mean curvature flow leading to a clear simplified proof of Brakke's main regularity theorem for this special case.... [The] author gives a detailed account of techniques for the study of singularities and expresses the underlying i

Probabilistic Theory of Mean Field Games
📁 Probabilistic Theory of Mean Field Games with Applications I: Mean Field FBSDEs, Control, and Games
✍ René Carmona,François Delarue (auth.) 📂 Library 📅 2018 🏛 Springer International Publishing 🌐 English

<p><p>This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions.</p>Volume