SpringerBriefs in Mathematics

Mean Field Games and Mean Field Type Control Theory

Authors: Bensoussan, Alain, Frehse, Jens, Yam, Phillip

  • ​This is the first contribution of this work to present a unified approach for both problems, using either HJB and FP coupled equations or stochastic maximum principle
  • ​Subject matter is interesting and has received much recent attention
  • Gives an overview of the mean-field game and mean-field type control problems
see more benefits

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-1-4614-8508-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-1-4614-8507-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this book

​Mean field games and Mean field type control introduce new problems in Control Theory. The terminology “games” may be confusing. In fact they are control problems, in the sense that one is interested in a single decision maker, whom we can call the representative agent. However, these problems are not standard, since both the evolution of the state and the objective functional is influenced but terms which are not directly related to the state or the control of the decision maker. They are however, indirectly related to him, in the sense that they model a very large community of agents similar to the representative agent. All the agents behave similarly and impact the representative agent. However, because of the large number an aggregation effect takes place. The interesting consequence is that the impact of the community can be modeled by a mean field term, but when this is done, the problem is reduced to a control problem. ​

Reviews

From the book reviews:

“This brief monograph is a presentation of some aspects of MFG theory and of a related class of problems, called mean field type control, where the state of the control system is driven by a McKean-Vlasov equation, namely, a stochastic differential equation where the drift depends also on the distribution of the state itself. … I believe the book should be mandatory reading for all mathematicians and engineers working in the field of MFG and related topics.” (Martino Bardi, Mathematical Reviews, November, 2014)

Table of contents (10 chapters)

  • Introduction

    Bensoussan, Alain (et al.)

    Pages 1-5

  • General Presentation of Mean Field Control Problems

    Bensoussan, Alain (et al.)

    Pages 7-9

  • The Mean Field Games

    Bensoussan, Alain (et al.)

    Pages 11-14

  • The Mean Field Type Control Problems

    Bensoussan, Alain (et al.)

    Pages 15-29

  • Approximation of Nash Games with a Large Number of Players

    Bensoussan, Alain (et al.)

    Pages 31-43

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-1-4614-8508-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-1-4614-8507-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Mean Field Games and Mean Field Type Control Theory
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Alain Bensoussan, Jens Frehse, Phillip Yam
eBook ISBN
978-1-4614-8508-7
DOI
10.1007/978-1-4614-8508-7
Softcover ISBN
978-1-4614-8507-0
Series ISSN
2191-8198
Edition Number
1
Number of Pages
X, 128
Topics