Mean-field limits for entropic multi-population dynamical systems

TL;DR

This paper proves the well-posedness and convergence of entropic multi-population dynamical systems to a mean-field limit, considering different time scales and coupling position evolution with label optimization.

Contribution

It establishes the first rigorous analysis of mean-field limits for multi-population systems with entropy regularization and multi-scale label dynamics.

Findings

Proved well-posedness of the multi-population system.

Established convergence to a mean-field approximation.

Analyzed systems with different time scales for positions and labels.

Abstract

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.