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Mean Field Games and Mean Field Type Control Theory: SpringerBriefs in Mathematics

Autor Alain Bensoussan, Jens Frehse, Phillip Yam
en Limba Engleză Paperback – 17 oct 2013
​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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Specificații

ISBN-13: 9781461485070
ISBN-10: 146148507X
Pagini: 140
Ilustrații: X, 128 p.
Dimensiuni: 155 x 235 x 7 mm
Greutate: 0.2 kg
Ediția:2013
Editura: Springer
Colecția Springer
Seria SpringerBriefs in Mathematics

Locul publicării:New York, NY, United States

Public țintă

Research

Cuprins

​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.

Recenzii

From the book reviews:
“This brief monograph is a presentation of some aspects of MFG theory and of a related class of problems, called mean field type control, where the state of the control system is driven by a McKean-Vlasov equation, namely, a stochastic differential equation where the drift depends also on the distribution of the state itself. … I believe the book should be mandatory reading for all mathematicians and engineers working in the field of MFG and related topics.” (Martino Bardi, Mathematical Reviews, November, 2014)

Caracteristici

This is the first contribution of this work to present a unified approach for both problems, using either HJB and FP coupled equations or stochastic maximum principle Subject matter is interesting and has received much recent attention Gives an overview of the mean-field game and mean-field type control problems