Probability Theory and Stochastic Modelling

Probabilistic Theory of Mean Field Games with Applications I

Mean Field FBSDEs, Control, and Games

Authors: Carmona, Rene, Delarue, Francois

  • First comprehensive presentation of state of the art theory of mean field games with special emphasis on the probabilistic approach
  • Numerous applications with explicit examples including numerical solutions
  • Self-contained treatment of related topics such as analysis on Wasserstein space and mean field control problems
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eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-319-58920-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.50
price for USA in USD
  • ISBN 978-3-319-56437-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic mean field control problems. 

Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.

Table of contents (7 chapters)

  • Learning by Examples: What Is a Mean Field Game?

    Carmona, René (et al.)

    Pages 3-65

  • Probabilistic Approach to Stochastic Differential Games

    Carmona, René (et al.)

    Pages 67-127

  • Stochastic Differential Mean Field Games

    Carmona, René (et al.)

    Pages 129-213

  • FBSDEs and the Solution of MFGs Without Common Noise

    Carmona, René (et al.)

    Pages 215-345

  • Spaces of Measures and Related Differential Calculus

    Carmona, René (et al.)

    Pages 349-512

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-319-58920-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.50
price for USA in USD
  • ISBN 978-3-319-56437-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Probabilistic Theory of Mean Field Games with Applications I
Book Subtitle
Mean Field FBSDEs, Control, and Games
Authors
Series Title
Probability Theory and Stochastic Modelling
Series Volume
83
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-58920-6
DOI
10.1007/978-3-319-58920-6
Hardcover ISBN
978-3-319-56437-1
Series ISSN
2199-3130
Edition Number
1
Number of Pages
XXVI, 714
Topics