# Intertemporal Choice and Its Anomalies

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Volume 2 of this Research Topic is available here: Mathematical models for intertemporal choice

Intertemporal choice consists ...

Volume 2 of this Research Topic is available here: Mathematical models for intertemporal choice

Intertemporal choice consists in the description and analysis of human behaviour in decision-making whereby an individual prefers a smaller and more immediate reward, or a bigger and more delayed outcome. This choice depends on the impatience exhibited by the subject in the way that the first option shows a more impatient behaviour than the second one. However, some individuals change their preferences when the two rewards are delayed by the same time interval. This change of preference can be explained by a variation (mainly, increase or decrease) of the impatience level giving rise to the concept of impulsivity (against self-control). A noteworthy concept related to impulsivity is subadditivity and superadditivity, meaning that upon splitting the time interval into smaller subintervals, discounting de- or increases.

This topic has been treated from the point of view of economics, psychology, sociology, medicine (diseases and addictions), and other fields. This multidisciplinary treatment of impatience and impulsivity has led to the searching of new models able to fit the wide variety of numerical information coming from the questionnaires passed to the different groups of interest (according to gender, marital status, geographical area, academic training, etc.). In this way, last papers on intertemporal choice have proposed some extensions of existing discount functions by using some tools coming from psychology (the perception of time), from statistics (the hazard rate of a system) or the mathematics (the deformation or the distortion of time). Additionally, these topics can be approached by using preferences on utilities, discount functions or delay functions as fundamental tools. Therefore, it is necessary to build a bridge between all areas of interest and all mathematical tools that can describe and quantify all possible choice alternatives.

In this Research Topic, we will focus on the treatment of intertemporal choice and its related concepts from a mathematical point of view. We expect mathematics (algebra, calculus, probability, statistics, topology, etc.) to be the bridge required to relate and unify all the approaches raised in last years. Some essential concepts involved in potential contributions can be the instantaneous discount rate, the discount factor, etc.

Additionally, the issue of intertemporal choice can be studied from the point of view of anomalies which can be defined as certain real situations which violate the axioms of the normative theory (the discounted utility model). The main anomalies are the delay effect, the magnitude effect, the sign effect, the improving sequence effect, the delay-speedup asymmetry effect and the spreading effect. Indeed, the analysis of these and other anomalies (like the peanuts effect) from a mathematical point of view will be a milestone in the progress of the knowledge of these paradoxes to advance in a satisfactory completion of the normative model.

Keywords: Intertemporal choice, anomalies, impatience, inconsistency, discount function

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