Exponential Versus Hyperbolic Discounting of Delayed Outcomes: Risk and Waiting Time

Frequently, animals must choose between more immediate, smallerrewards and more delayed, but larger rewards. For example, theyoften must decide between accepting a smaller prey item versuscontinuing to search for a larger one, or between entering aleaner patch versus travelling to a richer patch that is furtheraway. In both situations, choice of the more immediate, butsmaller reward may be interpreted as implying that the valueof the later reward is discounted; that is, the value of thelater reward decreases as the delay to its receipt increases.This decrease in value may occur because of the increased riskinvolved in waiting for rewards, or because of the decreasedrate of reward associated with increased waiting time. The presentresearch attempts to determine the form of the relation betweenvalue and delay, and examines implications of this relationfor mechanisms underlying risk-sensitive foraging. Two accounts of the relation between value and delay have beenproposed to describe the decrease in value resulting from increasesin delay: an exponential model and a hyperbolic model. Our researchdemonstrates that, of the two, a hyperbola-like discountingmodel consistently explains more of the variance in temporaldiscounting data at the group level and, importantly, at theindividual level as well. We show mathematically that the hyperbolicmodel shares fundamental features with models of prey and patchchoice. In addition, the present review highlights the implicationsof a psychological perspective for the behavioral biology ofrisksensitive foraging, as well as the implications of an ecologicalperspective for the behavioral psychology of risk-sensitivechoice and decision-making.