  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for the softmax part has been replaced by a rational one that includes the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.
