Mean Field Games and Mean Field Type Control Theory

Beschreibung

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. 
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

Autor*in

Alain Bensoussan

Themen in »Mean Field Games and Mean Field Type Control Theory«

Differential Games Dynamic Programming Mean Field Games Mean Field type control Nash equilibrium Stochastic Maximum Principle partial differential equations

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