A comparison between Tsallis’s statistics-based and generalized quasi-hyperbolic discount models in humans

Intertemporal choice has drawn attention in econophysics and neuroeconomics. Both impulsivity and inconsistency in intertemporal choice can be parametrized with a Tsallis’s statistics-based q-exponential discount model. Although a recent neuroeconomic study has proposed a dual-self discounting model (a generalized quasi-hyperbolic discounting), no study to date has examined the relationship between the q-exponential and quasi-hyperbolic models. We empirically estimated the inconsistency parameter 1−q in the q-exponential discount function and the parameter of an internal conflict between dual selves in intertemporal choice by humans. We observed that (i) the inconsistency parameter in the q-exponential model is positively related to a conflict between selves within a subject and (ii) q-exponential discounting better fits group data, while quasi-hyperbolic discounting better fits individual data. Our results indicate that (i) inconsistent intertemporal decision-makers may experience strong internal conflict during intertemporal choice behavior, and (ii) the q-exponential and the quasi-hyperbolic discount models should respectively be utilized for group and individual data. The usefulness of the q-exponential and the quasi-hyperbolic in studies of addiction and economic behavior is discussed.