2024/02/21 by Hidekazu Yoshioka, Yoshioka, Hidekazu, Motoh Tsujimura +3
Decision Sciences · Economics, Econometrics and Finance · #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Probability and Risk Models #Stochastic processes and financial applications #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2402.13453
openalex publication_date 2024/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The classical logit dynamic on a continuous action space for decision-making un-der uncertainty is generalized to the dynamic where the exponential function for the softmax part has been replaced by a rational one that includes the former as a special case. We call the new dynamic as the rational logit dynamic. The use of the rational logit function implies that the uncertainties have a longer tail than that assumed in the classical one. We show that the rational logit dynamic admits a unique measure-valued solution and the solution can be approximated using a fi-nite difference discretization. We also show that the vanishing-noise limit of the rational logit dynamic exists and is different from the best-response one, demon-strating that influences of the uncertainty tail persist in the rational logit dynamic. We finally apply the rational logit dynamic to a unique fishing competition data that has been recently acquired by the authors.