Domain independence and stability in young and older adults' discounting of delayed rewards

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 (Jimura et al., 2009), 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.     

Estimating the subjective value of future rewards: comparison of adjusting-amount and adjusting-delay procedures

The present study examined whether equivalent discounting of delayed rewards is observed with different experimental procedures. If the underlying decision-making process is the same, then similar patterns of results should be observed regardless of procedure, and similar estimates of the subjective value of future rewards (i.e., indifference points) should be obtained. Two experiments compared discounting on three types of procedure: adjusting-delay (AD), adjusting-immediate-amount (AIA), and adjusting-delayed-amount (ADA). For the two procedures for which discounting functions can be established (i.e., AD and AIA), a hyperboloid provided good fits to the data at both the group and individual levels, and individuals' discounting on one procedure tended to be correlated with their discounting on the other. Notably, the AIA procedure produced the more consistent estimates of the degree of discounting, and in particular, discounting on the AIA procedure was unaffected by the order in which choices were presented. Regardless of which of the three procedures was used, however, similar patterns of results were obtained: Participants systematically discounted the value of delayed rewards, and robust magnitude effects were observed. Although each procedure may have its own advantages and disadvantages, use of all three types of procedure in the present study provided converging evidence for common decision-making processes underlying the discounting of delayed rewards.     

Will travel for food: spatial discounting in two new world monkeys

Nonhuman animals steeply discount the future, showing a preference for small, immediate over large, delayed rewards. Currently unclear is whether discounting functions depend on context. Here, we examine the effects of spatial context on discounting in cotton-top tamarins (Saguinus oedipus) and common marmosets (Callithrix jacchus), species known to differ in temporal discounting. We presented subjects with a choice between small, nearby rewards and large, distant rewards. Tamarins traveled farther for the large reward than marmosets, attending to the ratio of reward differences rather than their absolute values. This species difference contrasts with performance on a temporal task in which marmosets waited longer than tamarins for the large reward. These comparative data indicate that context influences choice behavior, with the strongest effect seen in marmosets who discounted more steeply over space than over time. These findings parallel details of each species' feeding ecology. Tamarins range over large distances and feed primarily on insects, which requires using quick, impulsive action. Marmosets range over shorter distances than tamarins and feed primarily on tree exudates, a clumped resource that requires patience to wait for sap to exude. These results show that discounting functions are context specific, shaped by a history of ecological pressures.     

The subjective value of delayed and probabilistic outcomes: Outcome size matters for gains but not for losses

The subjective value of a reward (gain) is related to factors such as its size, the delay to its receipt and the probability of its receipt. We examined whether the subjective value of losses was similarly affected by these factors in 128 adults. Participants chose between immediate/certain gains or losses and larger delayed/probabilistic gains or losses. Rewards of $100 were devalued as a function of their delay (“discounted”) relatively less than $10 gains while probabilistic $100 rewards were discounted relatively more than $10 rewards. However, there was no effect of outcome size on discounting of delayed or probabilistic losses. For delayed outcomes of each size, the degree to which gains were discounted was positively correlated with the degree to which losses were discounted, whereas for probabilistic outcomes, no such correlation was observed. These results suggest that the processes underlying the subjective valuation of losses are different from those underlying the subjective valuation of gains.     

Discounting of delayed hypothetical money, alcohol, and food

For drug-dependent individuals, drugs of abuse that are delayed in time are discounted more steeply than money delayed in time in a hypothetical choice task. The reasons for this finding are not clear. This study examined whether steep discounting of drugs relative to money might be related to the function of drugs as primary/consumable reinforcers and money as a conditioned/non-consumable reinforcer. Twenty adults with no self-reported problems with money, alcohol, or food participated. They indicated their preferences for three hypothetical outcome types: delayed versus immediate money, delayed versus immediate food, and delayed versus immediate alcohol. Both the hyperbolic decay model and area under the curve analysis showed that money was discounted less steeply than alcohol or food, but that alcohol and food were discounted similarly. This finding replicates previous results showing that people without drug abuse problems show steep discounting of alcohol. Furthermore, this finding suggests that alcohol may be steeply discounted as part of a general process involving primary/consumable reinforcers, not necessarily because it is a drug.     

The present values of delayed rewards are approximately additive

In two experiments, human subjects were asked to estimate their present values of single delayed rewards and their present values of temporal sequences of three rewards. Present values were solicited by asking subjects to indicate an amount of money v for which they would be indifferent between receiving v at the end of the session and receiving the delayed reward(s). A procedure was used for which responding the true value of v was the optimal strategy, and the actual payoff that each subject received was determined by one randomly selected trial. In Experiment 1 (n=29) each delayed reward was 9.90 dollars in cash. In Experiment 2 (n=19) the delayed rewards were dated 15 dollars gift certificates to a local restaurant. In both experiments, the present values of the sequences were approximately equal to the sums of the present values of their component rewards. The presence of outliers suggests that a few subjects may have valued sequences less than the sums of their single rewards. Effects of a preference for uniform sequences, if any, were too small to be detected. Discounting of sequences was well fit by a parallel hyperbolic discounting equation, consistent with Mazur's [Mazur, J.E., 1986. Choice between single and multiple delayed reinforcers. J. Exp. Anal. Behav. 46 (1), 67-77] results using multiple reinforcers.     

Pathological gambling severity is associated with impulsivity in a delay discounting procedure

Research and clinical expertise indicates that impulsivity is an underlying feature of pathological gambling. This study examined the extent to which impulsive behavior, defined by the rate of discounting delayed monetary rewards, varies with pathological gambling severity, assessed by the South Oaks Gambling Screen (SOGS). Sixty-two pathological gamblers completed a delay discounting task, the SOGS, the Eysenck impulsivity scale, the Addiction Severity Index (ASI), and questions about gambling and substance use at intake to outpatient treatment for pathological gambling. In the delay discounting task, participants chose between a large delayed reward (US $1000) and smaller more immediate rewards (US $1-$999) across a range of delays (6h to 25 years). The rate at which the delayed reward was discounted (k value) was derived for each participant and linear regression was used to identify the variables that predicted k values. Age, gender, years of education, substance abuse treatment history, and cigarette smoking history failed to significantly predict k values. Scores on the Eysenck impulsivity scale and the SOGS both accounted for a significant proportion of the variance in k values. The predictive value of the SOGS was 1.4 times that of the Eysenck scale. These results indicate that of the measures tested, gambling severity was the best single predictor of impulsive behavior in a delay discounting task in this sample of pathological gamblers.     

The date-delay framing effect in temporal discounting depends on substance abuse

In the present study, individuals with substance use disorders (n=30) and non-addicted controls (n=30) were presented with a delay-discounting task with time being described either as dates or as temporal intervals. Three main results were obtained. First, in both groups reward size had a large impact on discounting future rewards, with discount rates becoming larger with smaller reward sizes. Second, participants discounted future rewards less strongly when their time of delivery was presented as a date instead of a temporal distance. Third, whereas discount rates of individuals with substance use disorders varied substantially with regard to the presentation of time in the task, the controls changed their choices depending on time presentation only slightly.     

The evolution of social discounting in hierarchically clustered populations

The expression of a social behaviour may affect the fitness of actors and recipients living in the present and in the future of the population. When there is a risk that a future reward will not be experienced in such a context, the value of that reward should be discounted; but by how much? Here, we evaluate social discount rates for delayed fitness rewards to group of recipients living at different positions in both space and time than the actor in a hierarchically clustered population. This is a population where individuals are grouped into families, families into villages, villages into clans, and so on, possibly ad infinitum. The group-wide fitness effects are assumed to either increase or decrease the fecundity or the survival of recipients and can be arbitrarily extended in space and time. We find that actions changing the survival of individuals living in the future are generally more strongly discounted than fecundity-changing actions for all future times and that the value of future rewards increases as individuals live longer. We also find that delayed fitness effects may not only be discounted by a constant factor per unit delay (exponential discounting), but that, as soon as there is localized dispersal in a population, discounting per unit delay is likely to fall rapidly for small delays and then slowly for longer delays (hyperbolic discounting). As dispersal tends to be localized in natural populations, our results suggest that evolution is likely to favour individuals that express present-biased behaviours and that may be time-inconsistent with respect to their group-wide effects.     

Prefrontal coding of temporally discounted values during intertemporal choice

Reward from a particular action is seldom immediate, and the influence of such delayed outcome on choice decreases with delay. It has been postulated that when faced with immediate and delayed rewards, decision makers choose the option with maximum temporally discounted value. We examined the preference of monkeys for delayed reward in an intertemporal choice task and the neural basis for real-time computation of temporally discounted values in the dorsolateral prefrontal cortex. During this task, the locations of the targets associated with small or large rewards and their corresponding delays were randomly varied. We found that prefrontal neurons often encoded the temporally discounted value of reward expected from a particular option. Furthermore, activity tended to increase with [corrected] discounted values for targets [corrected] presented in the neuron's preferred direction, suggesting that activity related to temporally discounted values in the prefrontal cortex might determine the animal's behavior during intertemporal choice.     

Rats bred for high alcohol drinking are more sensitive to delayed and probabilistic outcomes

Alcoholics and heavy drinkers score higher on measures of impulsivity than nonalcoholics and light drinkers. This may be because of factors that predate drug exposure (e.g. genetics). This study examined the role of genetics by comparing impulsivity measures in ethanol-naive rats selectively bred based on their high [high alcohol drinking (HAD)] or low [low alcohol drinking (LAD)] consumption of ethanol. Replicates 1 and 2 of the HAD and LAD rats, developed by the University of Indiana Alcohol Research Center, completed two different discounting tasks. Delay discounting examines sensitivity to rewards that are delayed in time and is commonly used to assess 'choice' impulsivity. Probability discounting examines sensitivity to the uncertain delivery of rewards and has been used to assess risk taking and risk assessment. High alcohol drinking rats discounted delayed and probabilistic rewards more steeply than LAD rats. Discount rates associated with probabilistic and delayed rewards were weakly correlated, while bias was strongly correlated with discount rate in both delay and probability discounting. The results suggest that selective breeding for high alcohol consumption selects for animals that are more sensitive to delayed and probabilistic outcomes. Sensitivity to delayed or probabilistic outcomes may be predictive of future drinking in genetically predisposed individuals.     

Delay discounting and gambling

Delay discounting describes the decline in the value of a reinforcer as the delay to that reinforcer increases. A review of the available studies revealed that steep delay discounting is positively correlated with problem or pathological gambling. One hypothesis regarding this correlation derives from the discounting equation proposed by Mazur (1989). According to the equation, steeper discounting renders the difference between fixed-delayed rewards and gambling-like variable-delayed rewards larger; with the latter being more valuable. The present study was designed to test this prediction by first assessing rats’ impulsive choices across four delays to a larger-later reinforcer. A second condition quantified strength of preference for mixed- over fixed-delays, with the duration of the latter adjusted between sessions to achieve indifference. Strength of preference for the mixed-delay alternative is given by the fixed delay at indifference (lower fixed-delay values reflect stronger preferences). Percent impulsive choice was not correlated with the value of the fixed delay at indifference and, therefore, the prediction of the hyperbolic model of gambling was not supported. A follow-up assessment revealed a significant decrease in impulsive choice after the second condition. This shift in impulsive choice could underlie the failure to observe the predicted correlation between impulsive choice and degree of preference for mixed- over fixed delays.     

The combined effects of delay and probability in discounting

Human discounting studies have frequently observed hyperbolic discounting of rewards that are delayed or probabilistic. However, no studies have systematically combined delay and probability in a single discounting procedure. Indifference points of hypothetical money rewards that are both delayed and probabilistic were determined. Probabilities were converted into comparable delays according to the h/k constant of proportionality determined by , and discounting rates were calculated. These data provided a very good fit to the hyperbolic model of discounting, suggesting that delay and probability can be combined into a single metric in studies of discounting. The inclusion of a magnitude condition found the Magnitude Effect commonly found in studies of temporal discounting. A temporal resolution of uncertainty condition found no effect. The present paper offers a novel statistical method, within an established framework, for the analysis of data from studies of discounting that combine delay and probability.     

Discounting of delayed hypothetical money and food: effects of amount

Delay discounting research determines how the value of an outcome is affected by delay to its receipt. Research so far shows that consumable outcomes are discounted more steeply by delay than money. Prior studies, however, have used large amounts of the outcomes (e.g. 100 dollars worth) that would not typically be consumed in one bout, unlike the corresponding amount of money (e.g. 100 dollars ). This experiment examined whether small amounts of food would be discounted more steeply than money, as occurs with larger amounts. One hundred and two adults indicated their preferences in a series of choices for two hypothetical outcome types: immediate versus delayed food and immediate versus delayed money. Participants made choices involving either relatively small maximum amounts of food (10 dollars worth) and money (10 dollars) or for relatively large maximum amounts of food (100 dollars worth) and money (100 dollars ). In the within-subject comparisons, food was discounted more steeply by delay than money for both groups. In the between-subject comparisons, different amounts of the commodities were affected similarly by delay. Overall, these results suggest that steeper discounting of consumable outcomes than money is a fairly robust phenomenon, occurring with relatively small amounts of outcomes as well as with larger amounts.     

Delay discounting and probability discounting as related to cigarette smoking status in adults

This study examined relations between adult smokers and non-smokers and the devaluation of monetary rewards as a function of delay (delay discounting, DD) or probability (probability discounting, PD). The extent to which individuals discount value, either as a function of a reward being delayed or probabilistic, has been taken to reflect individual differences in impulsivity. Those who discount most are considered most impulsive. Previous research has shown that adult smokers discount the value of delayed rewards more than adult non-smokers. However, in the one published study that examined probability discounting in adult smokers and non-smokers, the smokers did not discount the value of probabilistic rewards more than the non-smoker controls. From this past research, it was hypothesized that measures of delay discounting would differentiate between smokers and non-smokers but that probability discounting would not. Participants were 54 (25 female) adult smokers (n = 25) and non-smokers (n = 29). The smokers all reported smoking at least 20 cigarettes per day, and the non-smokers reported having never smoked. The results indicated that the smokers discounted significantly more than the non-smokers by both delay and probability. Unlike past findings, these results suggest that both delay and probability discounting are related to adult cigarette smoking; however, it also was determined that DD was a significantly stronger predictor of smoking than PD.     

Single units in the pigeon brain integrate reward amount and time-to-reward in an impulsive choice task

BACKGROUND: Animals prefer small over large rewards when the delays preceding large rewards exceed an individual tolerance limit. Such impulsive choice behavior occurs even in situations in which alternative strategies would yield more optimal outcomes. Behavioral research has shown that an animal's choice is guided by the alternative rewards' subjective values, which are a function of reward amount and time-to-reward. Despite increasing knowledge about the pharmacology and anatomy underlying impulsivity, it is still unknown how the brain combines reward amount and time-to-reward information to represent subjective reward value. RESULTS: We trained pigeons to choose between small, immediate rewards and large rewards delivered after gradually increasing delays. Single-cell recordings in the avian Nidopallium caudolaterale, the presumed functional analog of the mammalian prefrontal cortex, revealed that neural delay activation decreased with increasing delay length but also covaried with the expected reward amount. This integrated neural response was modulated by reward amount and delay, as predicted by a hyperbolical equation, of subjective reward value derived from behavioral studies. Furthermore, the neural activation pattern reflected the current reward preference and the time point of the shift from large to small rewards. CONCLUSIONS: The reported activity was modulated by the temporal devaluation of the anticipated reward in addition to reward amount. Our findings contribute to the understanding of neuropathologies such as drug addiction, pathological gambling, frontal lobe syndrome, and attention-deficit disorders, which are characterized by inappropriate temporal discounting and increased impulsiveness.     

Parameters of delay discounting assessment: number of trials, effort, and sequential effects.

Procedural variants in estimating delay discounting (DD) have been shown to yield significant within-subject differences in estimated degree of delay discounting as well as variations in the patterns of choice. The purpose of this study was to evaluate the effect of subject control over the number of trials in a delay discounting task, on degree of delay discounting. Participants were assessed with two computerized DD assessments: the full-length method presented participants with a fixed set of 240 trials, and the abbreviated task, where once participants had shown indifference between the immediate and delayed rewards, the remaining trials for that delay value were omitted. While the full-length and abbreviated methods did not differentially affect patterns of choice or estimated delay discounting, the order of presentation (ascending or descending) of immediate rewards produced differences in each measure: rate of delay discounting was significantly lower when estimated with the descending sequence; a larger proportion of area under the discounting curve was concentrated around the indifference point trial with the descending sequence; and a lower correlation was observed between estimates obtained across methods with the descending sequence.     

Delay discounting of saccharin in rhesus monkeys

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.     

Formal Comparison of Dual-Parameter Temporal Discounting Models in Controls and Pathological Gamblers

Temporal or delay discounting refers to the phenomenon that the value of a reward is discounted as a function of time to delivery. A range of models have been proposed that approximate the shape of the discount curve describing the relationship between subjective value and time. Recent evidence suggests that more than one free parameter may be required to accurately model human temporal discounting data. Nonetheless, many temporal discounting studies in psychiatry, psychology and neuroeconomics still apply single-parameter models, despite their oftentimes poor fit to single-subject data. Previous comparisons of temporal discounting models have either not taken model complexity into account, or have overlooked particular models. Here we apply model comparison techniques in a large sample of temporal discounting datasets using several discounting models employed in the past. Among the models examined, an exponential-power model from behavioural economics (CS model, Ebert & Prelec 2007) provided the best fit to human laboratory discounting data. Inter-parameter correlations for the winning model were moderate, whereas they were substantial for other dual-parameter models examined. Analyses of previous group and context effects on temporal discounting with the winning model provided additional theoretical insights. The CS model may be a useful tool in future psychiatry, psychology and neuroscience work on inter-temporal choice.