Characterizing the Jellinek curve using a discounting model with time deformations

This paper deals with the relationship between addiction/self-control and discount rates. In effect, it can be shown that the evaluation of temporal discounting is a candidate behavioral marker for addiction. More specifically, high discount rates are associated with several unhealthy behaviors (drinking, smoking and taking drugs, among them). There are also empirical studies that used a measure of delay discounting in order to predict abstinence or relapse. The main objective of this paper is to present a discounting model that describes the phases of addiction, vicious circles and recovery, present in the so-called Jellinek curve. To do this, we will start from the exponential discount function, which will be deformed, one or more times, by using the well-known Weber-Fechner and Stevens’ laws, in order to model the three aforementioned phases, specifically the relapse periods which characterize the vicious circles of the Jellinek curve. In this paper, we propose novel discount functions able to describe the behavior of addictions in all their phases and to fit intertemporal choice data in order to obtain the individuals’ discount rates.