Journal
MILAN JOURNAL OF MATHEMATICS
Volume 91, Issue 1, Pages 175-212Publisher
SPRINGER BASEL AG
DOI: 10.1007/s00032-022-00375-w
Keywords
Entropic regularization; Mean-field limit; Fast reaction limit; Population dynamics; Replicator-type dynamics; Superposition principle
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This paper proves the well-posedness of a multi-population dynamical system with an entropy regularization and its convergence to a suitable mean-field approximation, under a general set of assumptions. The case of different time scales between the agents' locations and labels dynamics is considered, with further assumptions on the evolution of the labels. 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.
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.
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