Probability Theory and Stochastic Modelling

Probabilistic Theory of Mean Field Games with Applications II

Mean Field Games with Common Noise and Master Equations

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
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eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-319-56436-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA in USD
  • ISBN 978-3-319-56435-7
  • 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 II tackles the analysis of mean field games in which the players are affected by a common source of noise. The first part of the volume introduces and studies the concepts of weak and strong equilibria, and establishes general solvability results. The second part is devoted to the study of the master equation, a partial differential equation satisfied by the value function of the game over the space of probability measures. Existence of viscosity and classical solutions are proven and used to study asymptotics of games with finitely many players.

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)

  • Optimization in a Random Environment

    Carmona, René (et al.)

    Pages 3-106

  • MFGs with a Common Noise: Strong and Weak Solutions

    Carmona, René (et al.)

    Pages 107-153

  • Solving MFGs with a Common Noise

    Carmona, René (et al.)

    Pages 155-235

  • The Master Field and the Master Equation

    Carmona, René (et al.)

    Pages 239-321

  • Classical Solutions to the Master Equation

    Carmona, René (et al.)

    Pages 323-446

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-319-56436-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA in USD
  • ISBN 978-3-319-56435-7
  • 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 II
Book Subtitle
Mean Field Games with Common Noise and Master Equations
Authors
Series Title
Probability Theory and Stochastic Modelling
Series Volume
84
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-56436-4
DOI
10.1007/978-3-319-56436-4
Hardcover ISBN
978-3-319-56435-7
Series ISSN
2199-3130
Edition Number
1
Number of Pages
XXIV, 700
Topics