Generalized logit dynamic defines a time-dependent integro-differential
equation with which a Nash equilibrium of an iterative game in a bounded and
continuous action space is expected to be approximated. We show that the use of
the exponential logit function is essential for the approximability, which will
not be necessarily satisfied with functions with convex exponential-like
functions such as q-exponential ones. We computationally analyze this issue and
discuss influences of the choice of the logit function through an application
to a fishing tourism problem in Japan