Mean Field Games and Mean Field Type Control Theory

Nonfiction, Science & Nature, Science, Other Sciences, System Theory, Mathematics, Statistics, Reference & Language, Reference
Cover of the book Mean Field Games and Mean Field Type Control Theory by Alain Bensoussan, Jens Frehse, Phillip Yam, Springer New York
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Author: Alain Bensoussan, Jens Frehse, Phillip Yam ISBN: 9781461485087
Publisher: Springer New York Publication: October 16, 2013
Imprint: Springer Language: English
Author: Alain Bensoussan, Jens Frehse, Phillip Yam
ISBN: 9781461485087
Publisher: Springer New York
Publication: October 16, 2013
Imprint: Springer
Language: English

​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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​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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