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Although the authors of a recent meta-analysis concluded there were no age-related differences in the discounting of delayed rewards, they did not examine the effects of income (Seaman et al., 2022). Accordingly, the present study compared discounting by younger and older adults (Ages 35-50 and 65-80) differing in household income. Two procedures were used: the Monetary Choice Questionnaire and the Adjusting-Amount procedure. Whereas no age difference was observed between the higher income (> $80,000) age groups, a significant difference was observed between younger and older adults with lower incomes (< $50,000): The younger adults discounted more steeply than the older adults. These findings, which were observed with both discounting procedures, support our buffering hypothesis, which assumes that the scarcity associated with a lower income is a stressor that can lead to steeper discounting, but that age-related increases in emotional stability can buffer such stressors, leading to age-related differences between lower income age groups. In contrast, no age difference was observed in higher income adults who experience much less scarcity. Further support for the buffering hypothesis comes from the finding that there was no age-related difference in discounting by the lower income groups when distress was statistically controlled. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

The vast majority of studies on discounting have focused on simple delayed outcomes, but most everyday decisions are more complicated. The present experiment focused on one such scenario, an iconic self-control situation in which immediate gains are followed by delayed losses. The same participants were studied in all conditions to permit examination of individual differences in choice behavior using intercorrelations and factor analysis. Consistent with previous research, the hyperboloid model accurately described the form of the discounting function and discounting was not affected by the amount of the delayed loss when it was presented alone. However, replicating other studies, smaller delayed losses were discounted more steeply than larger ones when presented in combination with immediate gains. Exploratory factor analysis revealed two factors, one loading primarily on loss-only conditions and the other loading primarily on conditions involving outcomes that combined gains and losses. These results imply that there are individual differences in how one combines gains and losses and that this characteristic of individual decision making might be an important predictor of decisions in the many everyday choice situations that involve complex outcomes., (© 2024 Society for the Experimental Analysis of Behavior.)

The present study compared the two most prominent procedures for measuring delay discounting, the Adjusting-Amount procedure and the Monetary Choice Questionnaire (MCQ). Of interest was whether the two procedures measure the same construct. Results obtained from two online samples recruited using the Prolific (N = 150) and MTurk (N = 243) platforms revealed generally similar results for both procedures. Regardless of the procedure, the sample, the reward amount, and whether the discounting measure used was theoretically based (i.e., log k) or was atheoretical (i.e., area under the curve, proportion of choices of the delayed reward option), the degree of discounting on the Adjusting-Amount procedure was highly correlated with the degree of discounting on the MCQ, consistent with the hypothesis that both procedures assess the same construct., Competing Interests: Declarations of interest None., (Copyright © 2023 Elsevier B.V. All rights reserved.)

Previous discounting research has focused on relatively simple situations (e.g., choosing between immediate and delayed gains, or between immediate and delayed losses) and the relations among amount, delay, and subjective value in such situations are now well established. Many everyday choice situations, however, are more complex, involving alternatives that combine gains and losses. In two experiments, participants discounted a monetary outcome that combined an immediate gain with a delayed loss. Consistent with the discounting framework, the value of the combination was approximately equal to the difference between the (undiscounted) value of the immediate gain and the (discounted) value of the delayed loss. More precise predictions of the relative subjective value of the delayed loss component of a combination were given by the same hyperboloid function that describes discounting in simple choice situations where outcomes only involve gains or losses, not both. As in previous studies, when the outcome was a simple one consisting of only a delayed loss, discounting was not affected by the amount of that loss. Surprisingly, however, when the loss was preceded by a gain, the degree to which the combination was discounted was affected by the amount of the loss. Notably, discounting of the delayed loss component of the combination decreased with the amount of the loss in a fashion similar to that observed with simple delayed gains, where smaller amounts are discounted more steeply than larger amounts. Choice situations involving immediate gains followed by delayed losses pose iconic self-control problems, and the present findings support the application of the discounting framework to these important everyday problems., (© 2022 Society for the Experimental Analysis of Behavior.)

Intertemporal choices require trade-offs between short-term and long-term outcomes. Ventromedial prefrontal cortex (vmPFC) damage causes steep discounting of future rewards (delay discounting [DD]) and impoverished episodic future thinking (EFT). The role of vmPFC in reward valuation, EFT, and their interaction during intertemporal choice is still unclear. Here, 12 patients with lesions to vmPFC and 41 healthy controls chose between smaller-immediate and larger-delayed hypothetical monetary rewards while we manipulated reward magnitude and the availability of EFT cues. In the EFT condition, participants imagined personal events to occur at the delays associated with the larger-delayed rewards. We found that DD was steeper in vmPFC patients compared to controls, and not modulated by reward magnitude. However, EFT cues downregulated DD in vmPFC patients as well as controls. These findings indicate that vmPFC integrity is critical for the valuation of (future) rewards, but not to instill EFT in intertemporal choice., Competing Interests: EC, FD, DK, JM, FB, VK, CC, LG, JM, SR No competing interests declared, (© 2021, Ciaramelli et al.)

Steep delay discounting is associated with problems such as addiction, obesity, and risky sexual behavior that are frequently described as reflecting impulsiveness and lack of self-control, but it may simply indicate poor cognitive functioning. The present investigation took advantage of the unique opportunity provided by the Human Connectome Project (N=1,206) to examine the relation between delay discounting and 11 cognitive tasks as well as the Big Five fundamental personality traits. With income level and education statistically controlled, discounting was correlated with only four of the 11 cognitive abilities evaluated, although the rs were all small (<.20). Importantly, the two discounting measures loaded on their own factor. Discounting was not correlated with Neuroticism or Conscientiousness, traits related to psychometric impulsiveness and self-control. These findings suggest that steep delay discounting is not simply an indicator of poor cognitive functioning or psychometric impulsiveness but an important individual difference characteristic in its own right.

Remembering and imagining specific, personal experiences can help shape our decisions. For example, cues to imagine future events can reduce delay discounting (i.e., increase the subjective value of future rewards). It is not known, however, whether such cues can also modulate other forms of reward discounting, such as probability discounting (i.e., the decrease in the subjective value of a possible reward as the odds against its occurrence increase). In addition, it is unclear whether there are age-related differences in the effects of cueing on either delay or probability discounting. Accordingly, young and older adult participants were administered delay and probability discounting tasks both with and without cues to imagine specific, personally meaningful events. As expected, cued episodic imagining decreased the discounting of delayed rewards. Notably, however, this effect was significantly less pronounced in older adults. In contrast to the effects of cueing on delay discounting, personally relevant event cues had little or no effect on the discounting of probabilistic rewards in either young or older adults; Bayesian analysis revealed compelling support for the null hypothesis that event cues do not modulate the subjective value of probabilistic rewards. In sum, imagining future events appears only to affect decisions involving delayed rewards. Although the cueing effect is smaller in older adults, nevertheless, it likely contributes to how adults of all ages evaluate delayed rewards and thus, it is, in fact, about time., Competing Interests: Declaration of competing interest None of the authors have any real or potential competing conflicts of interest to disclose that may influence the research and interpretation of the findings., (Copyright © 2020 Elsevier B.V. All rights reserved.)

A new probabilistic losses questionnaire as well as Kirby's delayed gains questionnaire and a previously developed delayed losses questionnaire were administered to a large online sample. Almost all participants showed the positive discounting choice pattern expected on the Kirby questionnaire, decreasing their choice of a delayed gain as time to its receipt increased. In contrast, approximately 15% of the participants showed negative discounting on the delayed losses questionnaire and/or the probabilistic losses questionnaire, decreasing their choice of an immediate loss as time to a delayed loss decreased and/or decreasing their choice of a certain loss as likelihood of the probabilistic loss increased. Mixture model analysis confirmed the existence of these negative discounting subgroups. The inconsistent findings observed in previous research involving delayed/probabilistic losses may be due to differences in the proportion of negative discounters who participated in previous studies. Further research is needed to determine how negative discounting of delayed and probabilistic losses manifests itself in everyday decisions. It should be noted that the presence of individuals who show atypical choice patterns when losses are involved may pose challenges for efforts to modify discounting in order to ameliorate behavioral problems, especially because many such problems concern choices that have negative consequences, often delayed and/or probabilistic., (© 2020 Society for the Experimental Analysis of Behavior.)

Discounting research has tended to focus on one simple situation, choice between an immediate, smaller gain and a larger, delayed gain, that is assumed by many to capture the essence of self-control. In everyday life, however, most choice situations are more complex, often involving combinations of gains and losses. We examined discounting in situations involving an immediate loss followed by a delayed gain that resulted in either a net gain (Experiment 1) or a net loss (Experiment 2) and compared it with discounting when there was only a delayed gain and no immediate loss. Larger delayed gains were discounted less steeply than smaller regardless of whether or not they were preceded by an immediate loss. Discounting functions of the same general hyperboloid form that describe the discounting of delayed gains in simple choice situations accurately described the discounting of combinations of gains and losses, although results differed depending on whether the combination would result in a net gain or a net loss. Participants consistently discounted loss-gain combinations less steeply than gains not preceded by an immediate loss when the combination represented a net loss (Experiment 2), but not when the combination represented a net gain (Experiment 1), a result analogous to the sign effect in simple choice situations (i.e., delayed gains are discounted more steeply than delayed losses). Taken together, these findings support the view that complicated choices like those common in everyday life can be understood within the discounting framework.

Background: Exposure to traumatic events is surprisingly common, yet little is known about its effect on decision making beyond the fact that those with post-traumatic stress disorder are more likely to have substance-abuse problems. We examined the effects of exposure to severe trauma on decision making in low-income, urban African Americans, a group especially likely to have had such traumatic experiences., Method: Participants completed three decision-making tasks that assessed the subjective value of delayed monetary rewards and payments and of probabilistic rewards. Trauma-exposed cases and controls were propensity-matched on demographic measures, treatment for psychological problems, and substance dependence., Results: Trauma-exposed cases discounted the value of delayed rewards and delayed payments, but not probabilistic rewards, more steeply than controls. Surprisingly, given previous findings that suggested women are more affected by trauma when female and male participants' data were analyzed separately, only the male cases showed steeper delay discounting. Compared with nonalcoholic males who were not exposed to trauma, both severe trauma and alcohol-dependence produced significantly steeper discounting of delayed rewards., Conclusions: The current study shows that exposure to severe trauma selectively affects fundamental decision-making processes. Only males were affected, and effects were observed only on discounting delayed outcomes (i.e. intertemporal choice) and not on discounting probabilistic outcomes (i.e. risky choice). These findings are the first to show significant differences in the effects of trauma on men's and women's decision making, and the selectivity of these effects has potentially important implications for treatment and also provides clues as to underlying mechanisms.

Huskinson et al. (2015) recently examined delay discounting in monkeys choosing between an immediate drug (cocaine) reinforcer and a delayed nondrug (food) reinforcer. The present experiment examined the reverse situation: choice between immediate nondrug (food) and delayed drug (cocaine) reinforcers. Whereas the former choice situation exemplifies drug abuse from a delay-discounting perspective, our interest in the latter choice situation is derived from the observation that drug abusers, who characteristically are associated with impulsive choice, typically must devote considerable time to procuring drugs, often at the expense of immediate nondrug alternatives. Accordingly, we analyzed 3 male rhesus monkeys' choices between immediate food and delayed cocaine (0.1 and 0.2 mg/kg/injection) using a hyperbolic model that allowed us to compare discounting rates between qualitatively different reinforcers. Choice of immediate food increased with food amount, and choice functions generally shifted leftward as delay to cocaine increased, indicating a decrease in the subjective value of cocaine. Compared with our previous delay-discounting experiment with immediate cocaine versus delayed food, both doses of delayed cocaine were discounted at a shallow rate. The present results demonstrate that rhesus monkeys will tolerate relatively long delays in an immediate-food versus delayed-drug situation, suggesting that in intertemporal choices between cocaine and food, the subjective value of cocaine is less affected by the delay until reinforcement than is the subjective value of delayed food. More generally, the present findings suggest that although drug abusers may choose impulsively when immediate drug reinforcement is available, they exercise self-control in the acquisition of a highly preferred, delayed drug reinforcer. (PsycINFO Database Record, ((c) 2016 APA, all rights reserved).)

Rationale: Steep discounting of delayed monetary rewards by substance-dependent individuals is well-established. Less is known, however, about discounting other kinds of outcomes, and very little is known about discounting by marijuana-dependent individuals., Objectives: To determine how cocaine-dependent individuals and marijuana-dependent individuals discount various delayed and probabilistic outcomes, both positive and negative., Methods: Marijuana-dependent individuals, cocaine-dependent individuals, and controls performed delay and probability discounting tasks with various hypothetical outcomes., Results: The cocaine-dependent (but not the marijuana-dependent) group discounted delayed liquid rewards and monetary gains, but not delayed losses, more steeply than the control group. In contrast, the marijuana-dependent group (but not the cocaine-dependent group) discounted delayed monetary losses more steeply than controls. There were no group differences in discounting for any of the probabilistic outcomes. Factor analysis revealed a delayed gain factor, a probabilistic gain factor, and a delayed/probabilistic loss factor. The delayed gain factor scores for the cocaine-dependent group, but not the marijuana-dependent group, differed significantly from those of the control group. The groups did not differ in their probabilistic gain factor scores, and the marijuana-dependent group did not differ from the controls with respect to their loss factor scores., Conclusions: These results are inconsistent with the idea that steep discounting of both gains and losses and both delayed and probabilistic outcomes reflects a general impulsivity trait, as well as with the idea that all drug-dependent individuals are steep discounters. Rather, differences in discounting appear to be related to both the type of outcome and the specific drug on which individuals are dependent.

Rationale: Alcohol dependence is known to be associated with steep discounting of delayed rewards, but its relation to the discounting of delayed losses and probabilistic rewards is unclear. Moreover, patterns of alcohol consumption vary considerably between communities, but previous research has not examined the relation between discounting and alcohol dependence in low-income African Americans., Objectives: The goal of the present study was to determine whether low-income, alcohol-dependent African Americans differ from controls in the degree to which they discount delayed rewards, delayed losses, or probabilistic rewards., Methods: African-American participants, both cases and controls, were recruited from the same low-income neighborhoods, and propensity-score matching was used to further control for demographic differences. Participants performed three tasks that assessed their discounting of hypothetical monetary outcomes: delayed rewards, delayed losses, and probabilistic rewards., Results: Alcohol-dependent cases discounted delayed gains, but not delayed losses or probabilistic gains, more steeply than their matched controls. The difference in discounting of delayed gains was localized to the male cases, whose discounting was steeper than either the male controls or the female cases; no gender difference was observed between male and female controls., Conclusions: The present results extend findings regarding discounting by substance abusers to a previously unstudied group, low-income African Americans, and suggest that in this group at least, alcohol dependence, particularly in males, may be more a reflection of choosing immediate rewards than of ignoring their delayed negative consequences.

How does the ability to imagine detailed future experiences (i.e., episodic prospection) contribute to choices between immediate and delayed rewards? Individuals with amnesia do not show abnormally steep discounting in intertemporal choice, suggesting that neither medial temporal lobe (MTL) integrity nor episodic prospection is required for the valuation of future rewards (Kwan et al. (), Hippocampus, 22:1215-1219; Kwan et al. (2013), J Exp Psychol, 142:1355-1369 2013). However, hippocampally mediated episodic prospection in healthy adults reduces the discounting of future rewards (Peters and Büchel (2010), Neuron, 66:138-148; Benoit et al. (2011), J Neurosci, 31:6771-6779), raising the possibility that MTL damage causes more subtle impairments to this form of decision-making than noted in previous patient studies. Intertemporal choice appears normal in amnesic populations, yet they may be unable to use episodic prospection to adaptively modulate the value assigned to future rewards. To investigate how the extended hippocampal system, including the hippocampus and related MTL structures, contributes to the valuation of future rewards, we compared the performance of six amnesic cases with impaired episodic prospection to that of 20 control participants on two versions of an intertemporal choice task: a standard discounting task, and a cued version in which cues prompted them to imagine specific personal future events temporally contiguous with the receipt of delayed rewards. Amnesic individuals' intertemporal choices in the standard condition were indistinguishable from those of controls, replicating previous findings. Surprisingly, performance of the amnesic cases in the cued condition indicates that amnesia does not preclude flexible modulation of choices in response to future event cues, even in the absence of episodic prospection. Cueing the personal future to modulate decisions appears to constitute a less demanding or a qualitatively different (e.g., personal semantic) form of prospection that is not as sensitive to MTL damage as prospective narrative generation., (© 2015 Wiley Periodicals, Inc.)

The value of an outcome is affected both by the delay until its receipt (delay discounting) and by the likelihood of its receipt (probability discounting). Despite being well-described by the same hyperboloid function, delay and probability discounting involve fundamentally different processes, as revealed, for example, by the differential effects of reward amount. Previous research has focused on the discounting of delayed and probabilistic rewards separately, with little research examining more complex situations in which rewards are both delayed and probabilistic. In 2 experiments, participants made choices between smaller rewards that were both immediate and certain and larger rewards that were both delayed and probabilistic. Analyses revealed significant interactions between delay and probability factors inconsistent with an additive model. In contrast, a hyperboloid discounting model in which delay and probability were combined multiplicatively provided an excellent fit to the data. These results suggest that the hyperboloid is a good descriptor of decision making in complicated monetary choice situations like those people encounter in everyday life., (PsycINFO Database Record (c) 2015 APA, all rights reserved.)

111 Participants, recruited from Amazon's MTurk worker pool, completed Kirby's (2009) monetary choice questionnaire, which involves choosing between immediate, but smaller rewards and delayed, but larger rewards. Individual participants' responses were scored in three ways: first, by calculating the proportion of choices of the delayed rewards; second; using the scoring procedure described by Kirby et al. (1999) to estimate discounting rate (i.e., the value of the k-parameter in a hyperbolic discounting function); and third, using logistic regression to estimate discounting rate (Wileyto et al., 2004). Individuals' scores calculated using the proportion measure and the logarithms of their estimated k values were very strongly correlated (rs>.97). In addition, the proportions of choices of small, medium, and large amounts of the delayed rewards were strongly correlated (rs>.80). Taken together, these results suggest that the relative ease of calculating the proportion measure does not require sacrificing reliability. Moreover, the proportion measure is atheoretical and very easy to calculate whereas estimating an individual's discounting rate requires assuming a theoretical model that may not be appropriate. Significant differences in the proportion of delayed reward choices were observed between the small, medium, and large delayed reward amounts, with smaller rewards being discounted more steeply than larger ones, replicating previous findings of magnitude effects. These results provide further validation of the proportion of delayed reward choices on the Kirby questionnaire as a measure of individual and group differences in discounting., (Copyright © 2014 Elsevier B.V. All rights reserved.)

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., (© Society for the Experimental Analysis of Behavior.)

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. [ABSTRACT FROM AUTHOR]

We examined the effect of holding reinforcement rate constant on delay discounting of hypothetical and real money when delays were actually experienced. In some conditions, participants were required to wait for the delayed rewards, and in some conditions, reinforcement rate was held constant by adding blackout periods after immediate rewards. Typical discounting occurred with the standard procedure and when there were no blackouts, but not when we held rate of reinforcement constant. Real and hypothetical money produced the same outcomes. [ABSTRACT FROM AUTHOR]

Deficits in episodic memory are associated with deficits in the ability to imagine future experiences (i.e., mental time travel). We show that K.C., a person with episodic amnesia and an inability to imagine future experiences, nonetheless systematically discounts the value of future rewards, and his discounting is within the range of controls in terms of both rate and consistency. Because K.C. is neither able to imagine personal uses for the rewards nor provide a rationale for selecting larger future rewards over smaller current rewards, this study demonstrates a dissociation between imagining and making decisions involving the future. Thus, although those capable of mental time travel may use it in making decisions about future rewards, these results demonstrate that it is not required for such decisions. © 2011 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Abstract: Individual discounting rates for different types of delayed reward are typically assumed to reflect a single, underlying trait of impulsivity. Recently, we showed that discounting rates are orders of magnitude steeper for directly consumable liquid rewards than for monetary rewards (), raising the question of whether discounting rates for different types of reward covary at the individual level. Accordingly, the present study examined the relation between discounting of hypothetical money and real liquid rewards in young adults (Experiment 1) and older adults (Experiment 2). At the group level, young adults discounted monetary rewards more steeply than the older adults, but there was no significant age difference with respect to liquid rewards. At the individual level, the rates at which young and older participants discounted each reward type were stable over a two- to fifteen-week interval (rs>70), but there was no significant correlation between the rates at which they discounted the two reward types. These results suggest that although similar decision-making processes may underlie the discounting of different types of rewards, the rates at which individuals discount money and directly consumable rewards may reflect separate, stable traits, rather than a single trait of impulsivity. [Copyright &y& Elsevier]

Pigeons' discounting of probabilistic and delayed food reinforcers was studied using adjusting-amount procedures. In the probability discounting conditions, pigeons chose between an adjusting number of food pellets contingent on a single key peck and a larger, fixed number of pellets contingent on completion of a variable-ratio schedule. In the delay discounting conditions, pigeons chose between an adjusting number of pellets delivered immediately and a larger, fixed number of pellets delivered after a delay. Probability discounting (i.e., subjective value as a function of the odds against reinforcement) was as well described by a hyperboloid function as delay discounting was (i.e., subjective value as a function of the time until reinforcement). As in humans, the exponents of the hyperboloid function when it was fitted to the probability discounting data were lower than the exponents of the hyperboloid function when it was fitted to the delay discounting data. The subjective values of probabilistic reinforcers were strongly correlated with predictions based on simply substituting the average delay to their receipt in each probabilistic reinforcement condition into the hyperboloid discounting function. However, the subjective values were systematically underestimated using this approach. Using the discounting function proposed by Mazur (1989), which takes into account the variability in the delay to the probabilistic reinforcers, the accuracy with which their subjective values could be predicted was increased. Taken together, the present findings are consistent with Rachlin's (Rachlin, 1990; Rachlin, Logue, Gibbon, & Frankel, 1986) hypothesis that choice involving repeated gambles may be interpreted in terms of the delays to the probabilistic reinforcers. [ABSTRACT FROM AUTHOR]

Abstract: Previously, we () showed that two-parameter hyperboloid models () provide significantly better fits to delay discounting data than simple, one-parameter hyperbolic and exponential models. Here, we extend this effort by comparing fits of the two-parameter hyperboloid models to data from a larger sample of participants (N =171) who discounted probabilistic as well as delayed rewards. In particular, we examined the effects of amount on the exponents in the two hyperboloid models of delay and probability discounting in order to evaluate key theoretical predictions of the standard psychophysical scaling interpretation of these exponents. Both the Rachlin model and the Green and Myerson model provided very good fits to delay and probability discounting of both small and large amounts at both the group and individual levels (all R 2s>.97 at the group level; all median R 2s>.92 at the individual level). For delay discounting, the exponent in both models did not vary as a function of delayed amount, consistent with the psychophysical scaling interpretation. For probability discounting, however, the exponent in both models increased as the probabilistic amount increased—a finding inconsistent with the scaling interpretation. [Copyright &y& Elsevier]

Abstract: The value of a reinforcer decreases as the time until its receipt increases, a phenomenon referred to as delay discounting. Although delay discounting of non-drug reinforcers has been studied extensively in a number of species, our knowledge of discounting in non-human primates is limited. In the present study, rhesus monkeys were allowed to choose in discrete trials between 0.05% saccharin delivered in different amounts and with different delays. Indifference points were calculated and discounting functions were established. Discounting functions for saccharin were well described by a hyperbolic function. Moreover, the discounting rates for saccharin in all six monkeys were comparable to those of other non-human animals responding for non-drug reinforcers. Also consistent with other studies of non-human animals, changing the amount of a saccharin reinforcer available after a 10-s delay did not affect its relative subjective value. Discounting functions for saccharin were steeper than we found in a previous study with cocaine, raising the possibility that drugs such as cocaine may be discounted less steeply than non-drug reinforcers. [Copyright &y& Elsevier]

Abstract: The present study compared four prominent models of delay discounting: a one-parameter exponential decay, a one-parameter hyperbola [Mazur, J.E., 1987. An adjusting procedure for studying delayed reinforcement. In: Commons, M.L., Mazur, J.E., Nevin, J.A., Rachlin, H. (Eds.), Quantitative Analyses of Behavior: The Effect of Delay and of Intervening Events on Reinforcement Value, vol. 5. Erlbaum, Hillsdale, NJ, pp. 55–73], a two-parameter hyperboloid in which the denominator is raised to a power [Green, L., Myerson, J., 2004. A discounting framework for choice with delayed and probabilistic rewards. Psychol. Bull. 130, 769–792], and a two-parameter hyperbola in which delay is raised to a power [Rachlin, H., 2006. Notes on discounting. J. Exp. Anal. Behav. 85, 425–435]. Sixty-four college undergraduates made choices between hypothetical monetary rewards, one immediate and one delayed, and the fit of the four models to their data was assessed. All four equations accounted for a large proportion of the variance at both the group and the individual levels, but the exponents of both two-parameter models were significantly less than 1.0 at the group level, and frequently so at the individual level. Taken together, these results strongly suggest that more than one parameter is needed to accurately describe delay discounting by humans. Notably, both the Rachlin and the Green and Myerson models accounted for more than 99% of the variance at the group level and for 96% of the variance in the median individual. Because both models provide such good descriptions of the data, model selection will need to be based on other grounds. [Copyright &y& Elsevier]