Mean Field Games and Mean Field Type Control Theory

Alain Bensoussan

ISBN 10: 146148507X / ISBN 13: 9781461485070

Verlag: Springer New York, Springer US Okt 2013, 2013

Beschreibung

Neuware -¿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.¿Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 140 pp. Englisch.

Bestandsnummer des Verkäufers 9781461485070

Bibliografische Details

• Titel: Mean Field Games and Mean Field Type Control Theory
• Verlag: Springer New York, Springer US Okt 2013
• Erscheinungsjahr: 2013
• Sprache: Englisch
• ISBN-10: 146148507X
• ISBN-13: 9781461485070
• Einband: Taschenbuch
• Zustand: Neu

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Inhaltsangabe

​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. ​

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