Computational analysis on a linkage between generalized logit dynamic and discounted mean field game
<|reference_start|>Computational analysis on a linkage between generalized logit dynamic and discounted mean field game: Logit dynamics are dynamical systems describing transitions and equilibria of actions of interacting players under uncertainty. An uncertainty is embodied in logit dynamic as a softmax type function often called a logit function originating from a maximization problem subjected to an entropic penalization. This study provides another explanation for the generalized logit dynamic, particularly its logit function and player's heterogeneity, based on a discounted mean field game subjected to the costly decision making of a representative player. A large discount limit of the mean field game is argued to yield a logit dynamic. Further, mean field games that lead to classical and generalized logit dynamics are clarified and their well posedness is discussed. Additionally, numerical methods based on a finite difference discretization for computing generalized logit dynamics and corresponding mean field games are presented. Numerical methods are applied to two problems arising in the management of resources and environment; one involves an inland fisheries management problem with legal and illegal anglers, while the other is a sustainable tourism problem. Particularly, cases that possibly lack the regularity condition to be satisfied for the unique existence of stationary solutions are computationally discussed.<|reference_end|>
@article{yoshioka2024computational,
    title={Computational analysis on a linkage between generalized logit dynamic
  and discounted mean field game},
    author={Hidekazu Yoshioka},
    journal={arXiv preprint arXiv:2405.15180},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.15180},
    primaryClass={math.OC cs.NA math.NA}
}