Mean Field Games and Mean Field Type Control Theory

  • Alain Bensoussan
  • Jens Frehse
  • Phillip Yam

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-x
  2. Alain Bensoussan, Jens Frehse, Phillip Yam
    Pages 1-5
  3. Alain Bensoussan, Jens Frehse, Phillip Yam
    Pages 7-9
  4. Alain Bensoussan, Jens Frehse, Phillip Yam
    Pages 11-14
  5. Alain Bensoussan, Jens Frehse, Phillip Yam
    Pages 15-29
  6. Alain Bensoussan, Jens Frehse, Phillip Yam
    Pages 31-43
  7. Alain Bensoussan, Jens Frehse, Phillip Yam
    Pages 45-57
  8. Alain Bensoussan, Jens Frehse, Phillip Yam
    Pages 59-66
  9. Alain Bensoussan, Jens Frehse, Phillip Yam
    Pages 67-87
  10. Alain Bensoussan, Jens Frehse, Phillip Yam
    Pages 89-97
  11. Alain Bensoussan, Jens Frehse, Phillip Yam
    Pages 99-124
  12. Back Matter
    Pages 125-128

About this book

Introduction

​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. ​

Keywords

Differential Games Dynamic Programming Mean Field Games Mean Field type control Nash equilibrium Stochastic Maximum Principle

Authors and affiliations

  • Alain Bensoussan
    • 1
  • Jens Frehse
    • 2
  • Phillip Yam
    • 3
  1. 1.Department of Systems Engineering and Engineering ManagementUniversity of Texas at Dallas Naveen Jindal School of Management, Richardson, Texas, USA, and City University of Hong KongKowloonHong Kong SAR
  2. 2.Universitat Bonn Institut für Angewandte MathematikBonnGermany
  3. 3.Department of StatisticsThe Chinese University of Hong KongShatinHong Kong SAR

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-8508-7
  • Copyright Information Alain Bensoussan, Jens Frehse, Phillip Yam 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-8507-0
  • Online ISBN 978-1-4614-8508-7
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • About this book
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