Mean-Field Limits for Entropic Multi-Population Dynamical Systems.

The well-posedness of a multi-population dynamical system with an entropy regularization and its convergence to a suitable mean-field approximation are proved, under a general set of assumptions. Under further assumptions on the evolution of the labels, the case of different time scales between the agents' locations and labels dynamics is considered. The limit system couples a mean-field-type evolution in the space of positions and an instantaneous optimization of the payoff functional in the space of labels.

Mean-Field Selective Optimal Control via Transient Leadership.

A mean-field selective optimal control problem of multipopulation dynamics via transient leadership is considered. The agents in the system are described by their spatial position and their probability of belonging to a certain population. The dynamics in the control problem is characterized by the presence of an activation function which tunes the control on each agent according to the membership to a population, which, in turn, evolves according to a Markov-type jump process.