Non-singularity of the generalized logit dynamic with an application to fishing tourism

TL;DR

This paper investigates the mathematical properties of the generalized logit dynamic in game theory, emphasizing the importance of the exponential logit function for approximating Nash equilibria, with an application to fishing tourism in Japan.

Contribution

It demonstrates the non-singularity of the generalized logit dynamic using exponential functions and analyzes the impact of logit function choice through a practical fishing tourism case study.

Findings

Exponential logit functions are essential for the dynamic's approximability.

Convex exponential-like functions may not satisfy the necessary conditions.

Application to Japanese fishing tourism illustrates the theoretical results.

Abstract

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.