Delay discounting refers to the decrease in subjective value of an outcome as the time to its receipt increases. Across species and situations, animals discount delayed rewards, and their discounting is well-described by a hyperboloid function. The current review begins with a comparison of discounting models and the procedures used to assess delay discounting in nonhuman animals. We next discuss the generality of discounting, reviewing the effects of different variables on the degree of discounting delayed reinforcers by nonhuman animals. Despite the many similarities in discounting observed between human and nonhuman animals, several differences have been proposed (e.g., the magnitude effect; nonhuman animals discount over a matter of seconds whereas humans report willing to wait months, if not years before receiving a reward), raising the possibility of fundamental species differences in intertemporal choice. After evaluating these differences, we discuss delay discounting from an adaptationist perspective. The pervasiveness of discounting across species and situations suggests it is a fundamental process underlying decision making.

The present study examined delay discounting of hypothetical monetary rewards over a wide range of amounts (from $20 to $10 million) in order to determine how reward amount affects the parameters of the hyperboloid discounting function and to compare fits of the hyperboloid model with fits of two discounting models used in neuroeconomics: the quasi-hyperbolic and the double-exponential. Of the three models assessed, the hyperboloid provided the best fit to the delay discounting data. The present delay discounting results may be compared to those of a previous study on probability discounting (Myerson, Green, & Morris, 2011) that used the same extended range of amounts. The hyperboloid function accurately described both types of discounting, but reward amount had opposite effects on the degree of discounting. Importantly, the amount of delayed reward affected the rate parameter of the hyperboloid discounting function but not its exponent, whereas the opposite was true for the amount of probabilistic reward. The finding that the exponent of the hyperboloid discounting function remains relatively constant across a wide range of delayed amounts provides strong support for a psychophysical scaling interpretation, and stands in stark contrast to the finding that the exponent of the hyperboloid function increases with the amount of probabilistic reward. Taken together, these findings argue that delay and probability discounting involve fundamentally different decision-making mechanisms.

The present study examined delay and probability discounting of hypothetical monetary losses over a wide range of amounts (from $20 to $500,000) in order to determine how amount affects the parameters of the hyperboloid discounting function. In separate conditions, college students chose between immediate payments and larger, delayed payments and between certain payments and larger, probabilistic payments. The hyperboloid function accurately described both types of discounting, and amount of loss had little or no systematic effect on the degree of discounting. Importantly, the amount of loss also had little systematic effect on either the rate parameter or the exponent of the delay and probability discounting functions. The finding that the parameters of the hyperboloid function remain relatively constant across a wide range of amounts of delayed and probabilistic loss stands in contrast to the robust amount effects observed with delayed and probabilistic rewards. At the individual level, the degree to which delayed losses were discounted was uncorrelated with the degree to which probabilistic losses were discounted, and delay and probability loaded on two separate factors, similar to what is observed with delayed and probabilistic rewards. Taken together, these findings argue that although delay and probability discounting involve fundamentally different decision-making mechanisms, nevertheless the discounting of delayed and probabilistic losses share an insensitivity to amount that distinguishes it from the discounting of delayed and probabilistic gains. Keywords delay discounting; probability discounting; losses; amount; hyperboloid; behavioral economics; humans Many everyday situations involve choosing between outcomes that differ in amount as well as in the delay until their occurrence or the likelihood of their occurrence. Such choices are important not just because of their consequences for people's lives but also because of their theoretical implications. Perhaps in recognition of the important life consequences of individuals' choice behavior, there is a rapidly growing literature on differences in the degree to which various groups of people (e.g., substance abusers, the elderly) discount the value of delayed or probabilistic outcomes (Madden & Bickel, 2010). From an individualdifferences perspective, researchers are seeking to understand the extent to which an Address correspondence to: Leonard Green, Washington University, Department of Psychology, Campus Box 1125, St. Louis, MO 63130, Phone: (314) lgreen@wustl individual's tendency to discount the value of outcomes that are delayed or probabilistic reflects a single underlying trait (e.g., impulsivity) or whether multiple traits are involved. In addition, there is a growing interest in how individuals make such choices, perhaps in recognition that the processes involved reflect fundamental decision-making mechanisms (e.g., Green & Myerson, 2013;van den Bos & McClure, 2013). Of course, these different lines of research can have important ...

Several studies have examined discounting by pigeons and rats using concurrent-chains procedures, but the results have been inconsistent. None of these studies, however, has established that discounting functions derived from estimates of indifference points can be obtained with a concurrent-chains procedure, so their validity remains in doubt. The present study used a concurrent-chains procedure within sessions combined with an adjusting-amount procedure across sessions to determine the present, subjective values of food reinforcers to be obtained after a delay. Discounting was well described by the hyperbolic discounting function, suggesting that the concurrent-chains procedure and the more typical adjusting-amount procedure are measuring the same process. Consistent with previous studies with rats and pigeons using adjusting-amount procedures, no significant effect of the amount of the delayed reinforcer on the degree of discounting was observed, suggesting that the amount effect may be unique to humans although consistent with the view that animals' choices are controlled by the relative, rather than the absolute, value of reinforcers.

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