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Regularity Theory for Mean-Field Game Systems

  • Book
  • © 2016

Overview

Authors:
  1. Diogo A. Gomes

    1. CEMSE Division, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia

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  2. Edgard A. Pimentel

    1. Department of Mathematics, Universidade Federal de Sao Carlos, São Carlos, Brazil

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    You can also search for this author in PubMed   Google Scholar

  3. Vardan Voskanyan

    1. CEMSE Division, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia

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    You can also search for this author in PubMed   Google Scholar

  • Details key elements of the regularity theory for mean-field games
  • Presents a series of techniques for well-posedness
  • Explores stationary and time-dependent MFGs through a series of a-priori estimates?
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Introduction

    • Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 1-8

  3. Explicit Solutions, Special Transformations, and Further Examples

    • Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 9-14

  4. Estimates for the Hamilton–Jacobi Equation

    • Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 15-37

  5. Estimates for the Transport and Fokker–Planck Equations

    • Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 39-61

  6. The Nonlinear Adjoint Method

    • Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 63-76

  7. Estimates for MFGs

    • Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 77-95

  8. A Priori Bounds for Stationary Models

    • Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 97-103

  9. A Priori Bounds for Time-Dependent Models

    • Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 105-109

  10. A Priori Bounds for Models with Singularities

    • Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 111-123

  11. Non-local Mean-Field Games: Existence

    • Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 125-130

  12. Local Mean-Field Games: Existence

    • Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 131-144

  13. Back Matter

    Pages 145-156
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Keywords

About this book

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.

Reviews

“This book is concerned with mean field game systems, or MFG systems for short. Such systems describe an infinite number of rational agents in competition. … The book is an accesible introduction to MFG systems, readable by anyone with a basic knowledge of partial differential equations.” (Teemu Lukkari, Mathematical Reviews, October, 2017)

Authors and Affiliations

  • CEMSE Division, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia

    Diogo A. Gomes, Vardan Voskanyan

  • Department of Mathematics, Universidade Federal de Sao Carlos, São Carlos, Brazil

    Edgard A. Pimentel

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