The effort required to obtain a rewarding outcome is an important factor in decision-making. Describing the reward devaluation by increasing effort intensity is substantial to understanding human preferences, because every action and choice that we make is in itself effortful. To investigate how reward valuation is affected by physical and cognitive effort, we compared mathematical discounting functions derived from research on discounting. Seven discounting models were tested across three different reward magnitudes. To test the models, data were collected from a total of 114 participants recruited from the general population. For one-parameter models (hyperbolic, exponential, and parabolic), the data were explained best by the exponential model as given by a percentage of explained variance. However, after introducing an additional parameter, data obtained in the cognitive and physical effort conditions were best described by the power function model. Further analysis, using the second order Akaike and Bayesian Information Criteria, which account for model complexity, allowed us to identify the best model among all tested. We found that the power function best described the data, which corresponds to conventional analyses based on the R2 measure. This supports the conclusion that the function best describing reward devaluation by physical and cognitive effort is a concave one and is different from those that describe delay or probability discounting. In addition, consistent magnitude effects were observed that correspond to those in delay discounting research.

Steeper delay discounting in substance abuse populations, compared to non-abusing populations, has been well-established in prior studies. Despite the growing interest in e-cigarettes as a novel and relatively understudied form of nicotine consumption, relatively little is known as to how e-cigarette users discount rewards compared to traditional cigarette smokers and never smokers. In the present study, we measured delay and probability discounting rates, as well as perceived risk inherent to a delayed reward, in current traditional cigarette smokers, e-cigarette users, and never smokers. We found that traditional cigarette smokers and e-cigarette users discounted delayed rewards at a similar rate—and both were steeper than never smokers. However, no differences were observed in probability discounting or in perceived risk inherent in reward delay.

Many day-today decisions may involve risky outcomes that occur at some delay after a decision has been made. We refer to such scenarios as delayed lotteries. Despite human choice often involves delayed lotteries, past research has primarily focused on decisions with delayed or risky outcomes. Comparatively, less research has explored how delay and probability interact to influence decisions. Within research on delayed lotteries, rigorous comparisons of models that describe choice from the discounting framework have not been conducted. We performed two experiments to determine how gain or loss outcomes are devalued when delayed and risky. Experiment 1 used delay and probability ranges similar to past research on delayed lotteries. Experiment 2 used individually calibrated delay and probability ranges. Ten discounting models were fit to the data using a genetic algorithm. Candidate models were derived from past research on discounting delayed or probabilistic outcomes. We found that participants' behavior was best described primarily by a threeparameter multiplicative model. Measures based on information criteria pointed to a solution in which only delay and probability were psychophysically scaled. Absolute measures based on residuals pointed to a solution in which amount, delay, and probability are simultaneously scaled. Our research suggests that separate scaling parameters for different discounting factors may not be necessary with delayed lotteries.

Empirical evidence suggests that mindfulness, psychological flexibility, and addiction are interrelated in decision making. In our study, we investigated the relationship of the behavioral profile, composed of mindfulness and psychological flexibility, and smoking status on delay and probability discounting. We demonstrated the interaction of the behavioral profile of mindfulness and psychological flexibility (lower or higher) and smoking status on delay discounting. We found that individuals who smoked and displayed higher mindfulness and psychological flexibility devalued rewards at a slower rate, compared to smokers with a lower profile. Importantly, in those with a higher profile, smokers discounted rewards no differently than nonsmokers. Smokers with a lower profile did display, however, increased impulsivity, compared to nonsmokers. These results suggest that behavioral interventions aiming to modify the behavioral profile with regard to mindfulness and psychological flexibility can indeed support the regulation of elevated impulsivity in smokers to equate with that of nonsmokers. In probability discounting, we observed that individuals with a higher profile displayed lower discounting rates, i.e., were less risk-averse, with no other significant main effect or interaction.

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