Probability Theory and Stochastic Modelling
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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 118,99 €
price for Spain (gross)
  • ISBN 978-3-319-58920-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 145,08 €
price for Spain (gross)
  • ISBN 978-3-319-56437-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 145,08 €
price for Spain (gross)
  • ISBN 978-3-030-13260-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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.

Reviews

“The text is very well-written and can be used to study the theory on various levels. It develops systematically from the wealth of motivating examples and heuristical considerations, through the carefully chosen collection of in-depth explained preliminaries, to the extensive nontrivial theory explained in full detail. … The book is highly recommended for those interested in the foundations and the up-to-date development of MFGs, as well as in the general area of stochastic control and related issues of analysis and probability.” (Vassili, Mathematical Reviews, January, 2019)

Table of contents (7 chapters)

Table of contents (7 chapters)
  • Learning by Examples: What Is a Mean Field Game?

    Pages 3-65

    Carmona, René (et al.)

  • Probabilistic Approach to Stochastic Differential Games

    Pages 67-127

    Carmona, René (et al.)

  • Stochastic Differential Mean Field Games

    Pages 129-213

    Carmona, René (et al.)

  • FBSDEs and the Solution of MFGs Without Common Noise

    Pages 215-345

    Carmona, René (et al.)

  • Spaces of Measures and Related Differential Calculus

    Pages 349-512

    Carmona, René (et al.)

Buy this book

eBook 118,99 €
price for Spain (gross)
  • ISBN 978-3-319-58920-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 145,08 €
price for Spain (gross)
  • ISBN 978-3-319-56437-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 145,08 €
price for Spain (gross)
  • ISBN 978-3-030-13260-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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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
Softcover ISBN
978-3-030-13260-6
Series ISSN
2199-3130
Edition Number
1
Number of Pages
XXVI, 714
Topics