Mean field games and mean field type control theory
 Author/Creator
 Bensoussan, Alain author.
 Language
 English.
 Publication
 New York : Springer, [2013].
 Physical description
 x, 128 pages : illustrations ; 24 cm.
 Series
 SpringerBriefs in mathematics.
Access
Available online

Stacks

Unknown
QC174.85 .M43 B45 2013

Unknown
QC174.85 .M43 B45 2013
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Contributors
 Contributor
 Frehse, J. (Jens), author.
 Yam, Phillip, author.
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 125126) and index.
 Includes bibliographical references and index.
 Contents

 Introduction
 General Presentation of Mean Field Control Problems
 Discussion of the Mean Field game
 Discussion of the Mean Field Type Control
 Approximation of Nash Games with a large number of players
 Linear Quadratic Models
 Stationary Problems Different Populations
 Nash differential games with Mean Field effect.
 Summary
 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.
Subjects
Bibliographic information
 Publication date
 2013
 Responsibility
 Alain Bensoussan, Jens Frehse, Phillip Yam.
 Series
 SpringerBriefs in Mathematics, 21918198
 ISBN
 9781461485070
 146148507X