Discounting of delayed rewards in opioid-dependent outpatients: exponential or hyperbolic discounting functions?
Madden GJ, Bickel WK, Jacobs EA
Department of Psychiatry,
University of Vermont, USA.
Exp Clin Psychopharmacol 1999 Aug;7(3):284-93


Recent theories of substance abuse have used value discounting of delayed rewards to partly explain the decision to take drugs. Normative-economic theory holds that an exponential function describes the effects of delay on discounting, whereas the matching law posits a hyperbolic discounting function. The ability of these functions to describe 18 human heroin-dependent individuals' monetary- and heroin-reward delay-discounting functions was assessed. In the 1st condition, participants chose between immediate and delayed hypothetical monetary rewards. Delayed rewards were $1,000, and the immediate reward amount was adjusted until choices reflected indifference. In the 2nd condition, participants chose between immediate and delayed heroin (the delayed amount was that which each participant reported he or she could purchase with $1,000). The hyperbolic function produced significantly higher R2 values and significantly lower sums of squared error values. Consistent with previous findings, delayed heroin rewards were discounted at a significantly higher rate than were delayed monetary rewards.
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