Abstract
The aim of this paper is to find a suitable discount function able to describe the progression of a certain addiction or disease under treatment as a discounting process. In effect, a certain indicator related to a disease decays over time in a manner which is mathematically similar to the way in which discounting has been modeled. We analyze the discount functions observed in experiments which study addictive and other problematic behaviors as well as some alternative hyperbola-like discount functions in order to fit the patience exhibited by the subject after receiving the treatment. Additionally, it has been experimentally found that people with addiction display high rates of discount (impatience) and preference reversals (dynamic inconsistency). This excessive discounting must be correctly modeled by a suitable discount function, otherwise, it can become a trans-disease process underlying addiction and other disorders. The (generalized) exponentiated hyperbolic discount function is proposed to describe the progression of a disease with respect to the treatment, since it maintains the property of inconsistency by exhibiting a decreasing discount rate after an initial period in which the opposite occurs.
Highlights
In a recent paper, Bickel et al (2012) state that drug-dependent individuals, and people with other diseases such as obesity, gambling problems, diagnosed ADHD (Attention Deficit Hiperactivity Disorder) or schizophrenia, discount delayed reinforcers more rapidly than individuals not having these addictions or diseases
It could be said that these individuals are more impulsive or impatient than individuals belonging to the control group
Many experimental studies have shown that the monetary discounting exhibited by people with certain addictions or diseases is best fitted to a hyperbolic discount function
Summary
In a recent paper, Bickel et al (2012) state that drug-dependent individuals, and people with other diseases such as obesity, gambling problems, diagnosed ADHD (Attention Deficit Hiperactivity Disorder) or schizophrenia, discount delayed reinforcers more rapidly than individuals not having these addictions or diseases. Bickel and Marsch (2001) broadly call them “personality assessments,” we will refer to impulsivity in the context of delay discounting Another interesting idea, proposed by Bickel et al (2012), is the consideration of excessive discounting as a trans-disease process underlying addiction and other disorders as well as disease-related behavior. The aforementioned characteristics will help us to find a suitable discount function able to describe these addiction situations To this end, this paper is organized as follows: In Section 2 we are going to describe a disease or an addiction as a discounting process.
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