Mean-field control of non exchangeable systems

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We study the optimal control of mean-field systems with heterogeneous and asymmetric interactions.

• This leads to considering a family of controlled Brownian diffusion processes with dynamics depending on the whole collection of marginal probability laws.
• We prove the well-posedness of such systems and define the control problem together with its related value function.
• We next prove a law invariance property for the value function which allows us to work on the set of collections of probability laws.