  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.
