Mean Field Games and Ideal Free Distribution.

Authors

Robert Stephen Cantrell, Chris Cosner, King-Yeung Lam, Idriss Mazari-Fouquer

Published in

Journal of mathematical biology. Volume 91. Issue 4. Pages 46. Sep 18, 2025. Epub Sep 18, 2025.

Abstract

The ideal free distribution in ecology was introduced by Fretwell and Lucas to model the habitat selection of animal populations. In this paper, we revisit the concept via a mean field game system with local coupling, which models a dynamic version of the habitat selection game in ecology. We establish the existence of classical solution of the ergodic mean field game system, including the case of heterogeneous diffusion when the underlying domain is one-dimensional and further show that the population density of agents converges to the ideal free distribution of the underlying habitat selection game, as the cost of control tends to zero. Our analysis provides a derivation of ideal free distribution in a dynamical context.

PMID:
40965693
Bibliographic data and abstract were imported from PubMed on 18 Sep 2025.

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