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Regularity Theory for Mean-Field Game Systems

  • Diogo A. Gomes
  • Edgard A. Pimentel
  • Vardan Voskanyan

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 1-8
  3. Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 9-14
  4. Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 15-37
  5. Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 39-61
  6. Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 63-76
  7. Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 77-95
  8. Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 97-103
  9. Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 105-109
  10. Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 111-123
  11. Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 125-130
  12. Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
    Pages 131-144
  13. Back Matter
    Pages 145-156

About this book

Introduction

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.

Keywords

Fokker-Planck equation Hamilton-Jacobi equation Lax-Hopf estimates Logarithmic non-linearities mean-field games stationary mean-field game problems

Authors and affiliations

  • Diogo A. Gomes
    • 1
  • Edgard A. Pimentel
    • 2
  • Vardan Voskanyan
    • 3
  1. 1.CEMSE DivisionKing Abdullah University of Science and TechnologyThuwalSaudi Arabia
  2. 2.Department of MathematicsUniversidade Federal de Sao CarlosSão CarlosBrazil
  3. 3.CEMSE DivisionKing Abdullah University of Science and TechnologyThuwalSaudi Arabia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-38934-9
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-38932-5
  • Online ISBN 978-3-319-38934-9
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site
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