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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. .

Mathematics. --- Nonlinear control theory. --- Stochastic control theory. --- System analysis. --- Mean field theory --- Control theory --- Game theory --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Control theory. --- Differential equations, Partial. --- Distribution (Probability theory) --- System theory. --- Systems, Theory of --- Systems science --- Distribution functions --- Frequency distribution --- Partial differential equations --- Partial differential equations. --- Probabilities. --- Systems Theory, Control. --- Probability Theory and Stochastic Processes. --- Partial Differential Equations. --- Science --- Characteristic functions --- Probabilities --- Dynamics --- Machine theory --- Philosophy --- Systems theory. --- Distribution (Probability theory. --- Differential equations, partial. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Mean field theory. --- Game theory.

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