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

A comparison between Tsallis' statistics-based and generalized quasi-hyperbolic discount models in humans. Acknowledgements: The research reported in this paper was supported by a grant from the Grant-in-Aid for Scientific Research (" 21st century center of excellence " grant) from the Ministry of Education, Culture, Sports, Science and Technology of Japan, and Yamaguchi endocrinological disorder research grant. Summary Intertemporal choice has drawn attention in econophysics and neuroeconomics. Both impulsivity and inconsistency in intertemporal choice can be parametrized with a Tsallis' 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 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) inconsistency parameter in the q-exponential model was positively related to a conflict between selves within a subject and (ii) q-exponential discounting better fit group data, while quasi-hyperbolic discounting better fit 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.