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＜電子ブック＞
Mean Field Games and Mean Field Type Control Theory / by Alain Bensoussan, Jens Frehse, Phillip Yam
(SpringerBriefs in Mathematics. ISSN:21918201)

版	1st ed. 2013.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2013
本文言語	英語
大きさ	X, 128 p : online resource
著者標目	*Bensoussan, Alain author Frehse, Jens author Yam, Phillip author SpringerLink (Online service)
件　名	LCSH:System theory LCSH:Control theory LCSH:Probabilities LCSH:Differential equations FREE:Systems Theory, Control FREE:Probability Theory FREE:Differential Equations
一般注記	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 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.  HTTP:URL=https://doi.org/10.1007/978-1-4614-8508-7

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