Delay, Probability, and Social Discounting in A Public Goods Game

A human social discount function measures the value to a person of a reward to another person at a given social distance. Just as delay discounting is a hyperbolic function of delay, and probability discounting is a hyperbolic function of odds-against, social discounting is a hyperbolic function of social distance. Experiment 1 obtained individual social, delay, and probability discount functions for a hypothetical $75 reward; participants also indicated how much of an initial $100 endowment they would contribute to a common investment in a public good. Steepness of discounting correlated, across participants, among all three discount dimensions. However, only social and probability discounting were correlated with the public-good contribution; high public-good contributors were more altruistic and also less risk averse than low contributors. Experiment 2 obtained social discount functions with hypothetical $75 rewards and delay discount functions with hypothetical $1,000 rewards, as well as public-good contributions. The results replicated those of Experiment 1; steepness of the two forms of discounting correlated with each other across participants but only social discounting correlated with the public-good contribution. Most participants in Experiment 2 predicted that the average contribution would be lower than their own contribution.     

Social discounting and delay discounting

Social discounting was measured as the amount of money a participant was willing to forgo to give a fixed amount (usually $75) to another person. In the first experiment, amount forgone was a hyperbolic function of the social distance between the giver and receiver. In the second experiment, degree of social discounting was an increasing function of reward magnitude whereas degree of delay discounting was a decreasing function of reward magnitude. In the third experiment, the shape of the function relating delayed rewards to equally valued immediate rewards for another person was predicted from individual delay and social discount functions. All in all, the studies show that the social discount function, like delay and probability discount functions, is hyperbolic in form. Copyright © 2007 John Wiley & Sons, Ltd.     

Now for Me,Later for Us? Effects of Group Context on Temporal Discounting

Delayed rewards are less valuable than immediate rewards. This well‐established finding has focused almost entirely on individual outcomes. However, are delayed rewards similarly discounted if they are shared by a group? The current article reports on three experiments exploring the effect of group context on delay discounting. Results indicate that discount rates of individual and group rewards were highly correlated, but that respondents were more willing to wait (decreased discounting) for shared outcomes than for individual outcomes. An explanatory model is proposed suggesting that decreased discount rates in group contexts may be due to the way the effects of both delay and social discounting are combined. That is, in a group context, a person values both a future reward (discounted by delay) and a present reward to another person (discounted by the social distance between them). The results are explained by a combined discount function containing a delay factor and a factor representing the social distance between the decision maker and group members. Practical implications of the fact that shared consequences can increase individual self‐control are also discussed. Copyright © 2011 John Wiley & Sons, Ltd.     

Social discounting of pain

Impatience can be formalized as a delay discount rate, describing how the subjective value of reward decreases as it is delayed. By analogy, selfishness can be formalized as a social discount rate, representing how the subjective value of rewarding another person decreases with increasing social distance. Delay and social discount rates for reward are correlated across individuals. However no previous work has examined whether this relationship also holds for aversive outcomes. Neither has previous work described a functional form for social discounting of pain in humans. This is a pertinent question, since preferences over aversive outcomes formally diverge from those for reward. We addressed this issue in an experiment in which healthy adult participants (N = 67) chose the timing and intensity of hypothetical pain for themselves and others. In keeping with previous studies, participants showed a strong preference for immediate over delayed pain. Participants showed greater concern for pain in close others than for their own pain, though this hyperaltruism was steeply discounted with increasing social distance. Impatience for pain and social discounting of pain were weakly correlated across individuals. Our results extend a link between impatience and selfishness to the aversive domain.     

Notes on discounting

In general, if a variable can be expressed as a function of its own maximum value, that function may be called a discount function. Delay discounting and probability discounting are commonly studied in psychology, but memory, matching, and economic utility also may be viewed as discounting processes. When they are so viewed, the discount function obtained is hyperbolic in form. In some cases the effective discounting variable is proportional to the physical variable on which it is based. For example, in delay discounting, the physical variable, delay (D), may enter into the hyperbolic equation as kD. In many cases, however, the discounting data are not well described with a single-parameter discount function. A much better fit is obtained when the effective variable is a power function of the physical variable (kDS in the case of delay discounting). This power-function form fits the data of delay, probability, and memory discounting as well as other two-parameter discount functions and is consistent with both the generalized matching law and maximization of a constant-elasticity-of-substitution utility     

The absence of numbers to express the amount may affect delay discounting with humans

Human delay discounting is usually studied with experimental protocols that use symbols to express delay and amount. In order to further understand discounting, we evaluated whether the absence of numbers to represent reward amounts affects discount rate in general, and whether the magnitude effect is generalized to nonsymbolic situations in particular. In Experiment 1, human participants were exposed to a delay‐discounting task in which rewards were presented using dots to represent monetary rewards (nonsymbolic); under this condition the magnitude effect did not occur. Nevertheless, the magnitude effect was observed when equivalent reward amounts were presented using numbers (symbolic). Moreover, in estimation tasks, magnitude increments produced underestimation of large amounts. In Experiment 2, participants were exposed only to the nonsymbolic discounting task and were required to estimate reward amounts in each trial. Consistent with Experiment 1, the absence of numbers representing reward amounts produced similar discount rates of small and large rewards. These results suggest that value of nonsymbolic rewards is a nonlinear function of amount and that value attribution depends on perceived difference between the immediate and the delayed nonsymbolic rewards.     

Charity Begins at Home: Cultural Differences in Social Discounting and Generosity

People often consider how their actions influence others when making decisions. However, we are not equally generous to everyone alike. Our willingness to share resources declines as a function of social distance between the decision maker and the recipient. This function is likely to be influenced by culture, but research on behavioral decision making is still lacking empirical evidence. In Western societies, individuals generally perceive themselves as autonomous and independent from others, whereas the distinction between self and close others is less sharply defined by Eastern individuals where relationships and group membership are more centralized. Therefore, the social discount function should reflect this difference in the distinction of self and others by a reduced decline in generosity over close social distances. A social decision‐making task was adapted to the intercultural context, and data were collected in Germany and China. For seven different social distances, we estimated how much money German and Chinese subjects were willing to forego to give a certain reward to another person. A hyperbolic model was fitted to the data. We found that other‐regarding generosity declines as a function of social distance independent of cultural identity. However, German subjects showed a marked drop in generosity across close social distances, which was significantly less pronounced in Chinese participants. Copyright © 2013 John Wiley & Sons, Ltd.     

Bidding for delayed rewards: Accumulation as delay discounting,delay discounting as regulation,demand functions as corollary

In the accumulation paradigm animals press one manipulandum to accumulate pellets or seconds of access to food, and then press another manipulandum, or run some distance, to collect it. The accumulation may be interpreted as delay discounting, with the animals adjusting the distal amount to compensate for its distance or delay. The amount accumulated before being collected is a linear function of the distance or time that the experimental paradigm stipulates for collecting it. That linear function follows from the Unit‐Price/Unit‐Amount axiom. The inverse of the linear compensation functions gives a delay‐discount hyperbola. The advantages of the accumulation paradigm and analytic framework for delay discounting studies are noted. Compensation functions are then derived from a behavioral regulation model, which generalizes them to contexts where the individual's budget for response cost becomes over‐taxed. In turn, such compensation/regulation models lead directly to representative demand functions. In sum, regulation models provide a theoretical grounding for demand functions, compensation functions, and delay discounting hyperbolas. The parameter that links them is the unit amount k, the slope of the compensation function and of the discount function, the setpoint for consumption in a regulation model, and the ideal quantity consumed at minimal price in a demand analysis.     

不确定性容忍度对跨期选择的影响及其情景依赖性

采用2(不确定性容忍度：高、低)×2(跨期日期：今天/14天、今天/180天)×2(延迟奖赏值：200元、1000元)混合实验设计,探讨不同任务特征下不确定性容忍度对跨期选择的影响。结果表明：跨期日期为180天时,不确定性容忍度主效应边缘显著;不确定性容忍度与延迟奖赏值交互作用显著：在200元时低容忍度个体对延迟奖赏的折扣程度大于高容忍度个体,在1000元时无此效应;跨期日期为14天时,不确定性容忍度的主效应及其与延迟奖赏值交互作用均不显著。这表明,不确定性容忍度对跨期选择存在影响,但这种影响受到跨期日期和延迟奖赏值的调节,具有情景依赖性。     

Smokers discount their drug of abuse in the same way as other consumable rewards

Recent research shows that drug abusers discount delayed monetary rewards more than nonabusers do, and they discount delayed substances of abuse (e.g., drugs) more than delayed money. Furthermore, non-drug-abusers discount food and substances of abuse (e.g., alcohol), more than money. Here, we compare the delay and probability discounting of money with that of a directly consumable reward (chocolate) and with that of a substance of abuse (cigarettes), in a drug-using population (smokers). In line with previous research, we found in two experiments that delay discounting differentiated between smokers and nonsmokers, and between money and a nonabused directly consumable reward (chocolate). In addition, our results show that there appears to be no difference in the extent to which smokers discount their abused substance compared to another directly consumable reward. These findings support the contention that drugs and food are part of the same category of primary reinforcers, whereas money is discounted differently, as a conditioned reinforcer.     

自闭症谱系障碍社交动机理论：机制及干预探索

自闭症谱系障碍(Autism Spectrum Disorder, ASD)表现为社会交往困难以及重复刻板兴趣或行为。社交动机理论提出ASD个体是由于社交动机缺乏导致的社交障碍。目前该理论缺乏理论元素及结构关系的系统论证, 及基于此理论的低龄ASD儿童群体的研究证据。本研究拟采用心理实验法、眼动及近红外脑成像技术, 探索低龄ASD儿童早期社交奖赏、社交定向异常眼动标记及眶额叶脑区活动的神经机制。此外, 通过音乐奖赏强化学习的干预方式改善该理论的核心元素(社交奖赏), 观测能否改善ASD儿童的社交动机。本研究的开展有望对该理论进行系统验证, 并形成改善社交行为的潜在干预方案。     

Delay discounting: I'm a k, you're a k

Delay discounting is the decline in the present value of a reward with delay to its receipt. Across a variety of species, populations, and reward types, value declines hyperbolically with delay. Value declines steeply with shorter delays, but more shallowly with longer delays. Quantitative modeling provides precise measures to characterize the form of the discount function. These measures may be regarded as higher-order dependent variables, intervening variables, or hypothetical constructs. I suggest the degree of delay discounting may be a personality trait. In the end, the ontological status of measures of delay discounting is irrelevant. Whatever delay discounting may be, its study has provided the field of behavior analysis and other areas measures with robust generality and predictive validity for a variety of significant human problems. Research on moderating the degree of delay discounting has the potential to produce substantial societal benefits.     

Changes in intertemporal choices in deviant behaviors

Delay discounting is the process of devaluing results that happen in the future. We present a comprehensive literature review of changes on intertemporal choices in deviant behaviors, namely in (a) substance-related and addictive disorders, (b) disruptive, impulse-control, and conduct disorders, and (c) eating disorders. We also present studies focused on differences in demographic characteristics of the populations by gender, age, and education/social class. Delay discounting is presented as a process of studying intertemporal choices, resulting from decades of empirical research. Studies indicate that this process may provide explanation as to why individuals will sometimes choose a smaller reward, available sooner, instead of a larger reward available later. When studying populations with the above-mentioned problems, they tend to exhibit more pronounced discounting functions than control groups. The association between discounting and gender is not clear. The relationship between delay discounting and age is relatively clear, where older individuals discount less markedly than younger individuals. Studies suggest that shallower discounting gradients are associated with higher levels of intelligence and academic success. We emphasize the need for more empirical research on delay discounting, especially in regard to deviant behavior that may be associated with impulse-control disorders.     

Discounting by Probabilistic Waiting

In everyday life, many probabilistic situations may be characterized as probabilistic waiting. A gambler, for example, bets repeatedly at the racetrack, the casino, or the card table. The gambler may not win on the first try, but if a gamble is repeated enough times, a win is almost certain to occur eventually. If repeated gambles are structured as strings of losses ending in a win (probabilistic waiting) and the amount won is discounted by the delay caused by the series of losses, then strings with many losses will be discounted more than those with fewer losses, thereby causing subjective value of the series of gambles as a whole to increase. The current study used the opposite effect that amount has on the degree of delay and probability discounting as a marker to determine whether people evaluate situations involving probabilistic waiting as they evaluate situations involving delayed outcomes or as situations involving probabilistic outcomes. We find that the more likely a probabilistic waiting situation is to end in reward (e.g., a gamble is repeated indefinitely until reward is obtained), the more that situation conforms to delay discounting; the less likely a probabilistic waiting situation is to end in reward (e.g., a fixed, small number of gambles), the more that situation conforms to probability discounting. We argue that the former situation is applicable to pathological gambling, and that people with steep delay discount functions would therefore be more likely to have gambling problems. Copyright © 2015 John Wiley & Sons, Ltd.     

The need of young adults to text now: Using delay discounting to assess informational choice

This study examined the value of responding immediately to a text or call and the ability to wait. The willingness to delay texting or calling for a larger monetary reward was compared with delay tolerance for monetary rewards alone. The results of two experiments showed no differences in the qualitative shape of the delay discounting functions, indicating a similar decision-making process for informational (texting or calling) and monetary decisions. Data in the second experiment showed that the degree of delay tolerance varied as a function of the social distance of the texting partner, indicating a strategic decision-making process in informational decisions. However, the time course of loss of value for informational versus monetary rewards revealed substantial quantitative differences. While money loses value on the time span of weeks, information loses value within minutes, which may explain why behaviors like texting often occur in inappropriate situations and may seem like addictions.     

Within-subject comparison of real and hypothetical money rewards in delay discounting

A within-subject design, using human participants, compared delay discounting functions for real and hypothetical money rewards. Both real and hypothetical rewards were studied across a range that included $10 to $250. For 5 of the 6 participants, no systematic difference in discount rate was observed in response to real and hypothetical choices, suggesting that hypothetical rewards may often serve as a valid proxy for real rewards in delay discounting research. By measuring discounting at an unprecedented range of real rewards, this study has also systematically replicated the robust finding in human delay discounting research that discount rates decrease with increasing magnitude of reward. A hyperbolic decay model described the data better than an exponential model.     

Rhesus monkeys lack a consistent peak-end effect

In humans, the order of receiving sequential rewards can significantly influence the overall subjective utility of an outcome. For example, people subjectively rate receiving a large reward by itself significantly higher than receiving the same large reward followed by a smaller one (Do, Rupert, & Wolford, 2008). This result is called the peak-end effect. A comparative analysis of order effects can help determine the generality of such effects across primates, and we therefore examined the influence of reward-quality order on decision making in three rhesus macaque monkeys (Macaca mulatta). When given the choice between a high–low reward sequence and a low–high sequence, all three monkeys preferred receiving the high-value reward first. Follow-up experiments showed that for two of the three monkeys their choices depended specifically on reward-quality order and could not be accounted for by delay discounting. These results provide evidence for the influence of outcome order on decision making in rhesus monkeys. Unlike humans, who usually discount choices when a low-value reward comes last, rhesus monkeys show no such peak-end effect.     

DISCOUNTING OF DELAYED REWARDS:

Abstract— In this study, children, young adults, and older adults chose between immediate and delayed hypothetical monetary rewards The amount of the delayed reward was held constant while its delay was varied All three age groups showed delay discounting, that is, the amount of an immediate reward judged to be of equal value to the delayed reward decreased as a function of delay The rate of discounting was highest for children and lowest for older adults, predicting a life-span developmental trend toward increased selfcontrol Discounting of delayed rewards by all three age groups was well described by a single function with agesensitive parameters (all R²s>94) Thus, even though there are quantitative age differences in delay discounting, the existence of an age-invanant form of discount function suggests that the process of choosing between rewards of different amounts and delays is qualitatively similar across the life span     

Delay discounting as impaired valuation: Delayed rewards in an animal obesity model

Obesity is a major public health problem, which, like many forms of addiction, is associated with an elevated tendency to choose smaller immediate rather than larger delayed rewards, a response pattern often referred to as excessive delay discounting. Although some accounts of delay discounting conceptualize this process as impulsivity (placing the emphasis on overvaluing the smaller immediate reward), others have conceptualized delay discounting as an executive function (placing the emphasis on delayed rewards failing to retain their value). The present experiments used a popular animal model of obesity that has been shown to discount delayed rewards at elevated rates (i.e., obese Zucker rats) to test two predictions that conceptualize delay discounting as executive function. In the first experiment, acquisition of lever pressing with delayed rewards was compared in obese versus lean Zucker rats. Contrary to predictions based on delay discounting as executive function, obese Zucker rats learned to press the lever more quickly than controls. In the second experiment, progressive ratio breakpoints (a measure of reward efficacy) with delayed rewards were compared in obese versus lean Zucker rats. Contrary to the notion that obese rats fail to value delayed rewards, the obese Zucker rats' breakpoints were (at least) as high as those of the lean Zucker rats.     

Hierarchical Bayesian estimation and hypothesis testing for delay discounting tasks

A state-of-the-art data analysis procedure is presented to conduct hierarchical Bayesian inference and hypothesis testing on delay discounting data. The delay discounting task is a key experimental paradigm used across a wide range of disciplines from economics, cognitive science, and neuroscience, all of which seek to understand how humans or animals trade off the immediacy verses the magnitude of a reward. Bayesian estimation allows rich inferences to be drawn, along with measures of confidence, based upon limited and noisy behavioural data. Hierarchical modelling allows more precise inferences to be made, thus using sometimes expensive or difficult to obtain data in the most efficient way. The proposed probabilistic generative model describes how participants compare the present subjective value of reward choices on a trial-to-trial basis, estimates participant- and group-level parameters. We infer discount rate as a function of reward size, allowing the magnitude effect to be measured. Demonstrations are provided to show how this analysis approach can aid hypothesis testing. The analysis is demonstrated on data from the popular 27-item monetary choice questionnaire (Kirby, Psychonomic Bulletin & Review, 16(3), 457–462 2009), but will accept data from a range of protocols, including adaptive procedures. The software is made freely available to researchers.