Method

Results

The indifference points obtained at each of the seven delays are shown in Table 1 under gambling and nongambling conditions for each participant. Within each assessment, the indifference points usually decreased or remained the same across successive delay values. Each obtained indifference curve was evaluated according to the following criteria to determine consistency with delay discounting, broadly construed. The mean of the indifference points from the three shortest delay conditions had to exceed the mean of the indifference points from the three longest delay conditions, and indifference points could not increase across successive delays more than once. The obtained indifference curves for all participants under all conditions met these criteria.

Table 1 also contains the empirically derived discounting parameters (k values) and the individual proportions of variance (R²) accounted for by the hyperbolic model for each participant under each condition. In general, the hyperbolic model provided an adequate description of the majority of the individual indifference curves. Across all participants and conditions, the median R² value was 0.86 and the interquartile range was 0.64 to 0.94. In 12 instances involving 9 participants, however, the proportion of variance accounted for by Equation 1 fell below 0.7. Such poor fits often occurred despite orderly indifference curves (e.g., see Participant 103 under the gambling condition). Thus, although Equation 1 adequately described most of the individual indifference curves, a subset of the indifference curves may not have been formally consistent with the hyperbolic model.

Nonetheless, the k parameter provides a useful index of degree of discounting, as higher k values indicate greater sensitivity to delay to reinforcement. If the gambling context increases the degree of delay discounting, then the k parameters derived from data collected in the gambling context should exceed those derived from data collected in the nongambling context. Data from the 11 participants for whom Equation 1 provided an adequate description (i.e., R² >0.7) of the indifference curves from both contexts are shown in Figure 1. For 10 of these 11 participants, the k value derived from data obtained in the gambling context exceeded that derived from data obtained in the nongambling context.

Area under the indifference curve (AUC), another measure of delay discounting, is also presented in Table 1 for each participant under both conditions. AUC is a theoretically neutral measure of delay discounting that requires no a priori assumptions regarding the form of the indifference curve (Myerson, Green, & Warusawitharana, 2001). As such, the AUC measure is applicable to a wider range of indifference curves than other quantitative models, such as those based on hyperbolic or exponential delay discounting, that make explicit assumptions regarding the form of the indifference curve. The AUC ranges from 0 (steep discounting) to 1 (little or no discounting).

If the gambling context exacerbates delay discounting, then the AUC obtained in the gambling context should be lower than the AUC obtained in the nongambling context. Indeed, for 16 of the 20 participants, the AUC was lower in the gambling context (see Figure 2). An analysis of variance was conducted to assess the effects of context and sequence of conditions on AUC. The effect of sequence was not statistically significant, F(1, 18)  =  2.4480, p  =  .14, nor was the interaction between sequence and context, F(1, 18)  =  0.0220, p  =  .88. However, the main effect of context on AUC was statistically significant, F(1, 18)  =  4.9788, p  =  .04.

Figure 3 shows aggregate discounting curves for all participants in gambling and nongambling contexts. The data points represent the medians of the individual indifference points at each delay (see Table 1). Equation 1 provided a good description of the aggregate indifference curves. The proportions of variance accounted for by the hyperbolic model were 0.96 and 0.93 in the gambling and nongambling contexts, respectively. The derived k value for the aggregate data was higher for participants in the gambling context (k  =  .0358) than in the nongambling context (k  =  .0171). The area under the aggregate curve was also smaller in the gambling context (AUC  =  .1762) than in the nongambling context (AUC  =  .3118).

Discussion

The current findings illustrate that most pathological gamblers discounted delayed rewards to a greater degree in a gambling context. For the majority of participants, k values derived from fitting Equation 1 to individual indifference curves were larger in the gambling context than in the nongambling context, indicating more severe discounting when gambling. It should be noted, however, that Equation 1 did not provide a good fit to the individual indifference curves for a number of participants, despite relatively orderly discounting data. Individual AUC measures were also smaller in the gambling context than in the nongambling context for the majority of participants, again demonstrating steeper temporal discounting when gambling. Aggregate data patterns were in accord with these individual patterns. However, the aggregate data were well described by Equation 1. Although previous research has demonstrated the utility of the hyperbolic model (Equation 1) to fit obtained discounting data (e.g., Kirby & Marakovic, 1995; Kirby, Petry, & Bickel, 1999; Madden et al., 1997; Mazur, 1987; Petry & Bickel, 1998; Rachlin et al., 1991; Raineri & Rachlin, 1993), our present findings revealed many instances in which this model provided a relatively poor fit to the obtained individual data. The difficulties we had with Equation 1 were similar to those reported by Dixon et al. (2003) in a comparison of delay discounting in pathological gamblers and matched controls and by Dixon et al. (2005) in a comparison of delay discounting in persons with acquired brain injuries and matched controls. As in these previous studies, AUC measures were deemed useful for data analysis. The strength of the AUC measure is that it is not tied to any particular theory about the form of the indifference curve (i.e., hyperbolic or exponential discounting). As such, it can be used to evaluate data that do not conform to existing quantitative models. One weakness of the AUC measure, however, is that similar areas may be obtained from very different discounting curves. Nonetheless, AUC analyses are gaining popularity for analyzing discounting data that may not fit hyperbolic decay functions (Dixon et al., 2003, 2005; Myerson et al., 2001), and future researchers may wish to compare the two metrics with various other clinical populations to further establish their concordance.

The present study also underscores the value of conducting within-participant analyses of variables that may affect intertemporal choice. Sixteen of our 20 participants showed greater degrees of delay discounting when assessed within a gambling environment compared to a nongambling environment. Although Figure 3 displays aggregate differences in discounting across contexts, the group analysis may obscure the magnitude and consistency of the effect. The individual data displayed in Table 1 and Figure 2 provide a more refined within-participant analysis of the subtle changes in discounting that occurred for each participant. For example, the interquartile ranges displayed in Figure 2 illustrate considerable overlap across contexts and could be considered an indication that the effect of context was not robust. However, it is the relative change that occurred within each individual participant's discounting pattern that should be considered our most important finding. Consider Participant 101, who displayed an AUC value of .08 in the gambling context and .21 in the nongambling context, and Participant 103, who displayed AUCs of .34 and .40 in those respective contexts. Both of Participant 101's AUCs were much higher than 103's (indicating generally greater discounting by 103), but the relative change within each participant was similar. This illustrates the true value of within-participant analysis. Although both participants had different degrees of delay discounting, each was relatively equally sensitive to the contextual manipulations of the present experiment.

The present findings add to a growing line of research on variables that affect delay discounting. Previous research has shown that severity of discounting can be affected by conditions of deprivation (Giordano et al., 2002), reinforcer magnitude (Green et al., 1997), reinforcer type (Bickel et al., 1999; Madden et al., 1997, 1999), and history (Bickel et al.). These findings are important because they suggest that such variables need to be controlled when conducting discounting assessments and they provide a rationale for conducting multiple assessments within individual participants.

The present data also further our understanding of the discounting behavior of pathological gamblers, who have been shown to discount to greater degrees than matched controls (Dixon et al., 2003; Petry & Casarella, 1999). Our data show that altering the context in which the delay-discounting task is completed can result in different degrees of discounting. To date, the impact of context on altering the behavior of pathological gamblers has only been speculative (Dixon et al., 2003); however, the current data demonstrate empirical support for this assertion.

The present study was conducted in a natural setting and, as such, suffers from some potential threats to internal validity that should be recognized. First, our sample may not have been representative of pathological gamblers in general. Participants were self-selected volunteers, and the method of identifying pathological gamblers relied on self-report rather than direct observation of relevant behavior. Although the SOGS is the primary screening instrument in the gambling literature, our sample may have been restricted to those pathological gamblers who responded accurately to the questionnaire. In addition, the sample may have included gamblers who underestimated the prevalence of their gambling. This sampling problem seems more likely in that many pathological gamblers may not wish to disclose the severity of their disorder to an unknown researcher. Furthermore, we used only pathological gamblers who were currently gambling and not seeking treatment for this disorder. Thus, our participants may actually represent the most severe type of pathological gambler, one who is currently gambling and not seeking treatment. Another potential confounding effect is that our current participants were free to consume alcohol within the gambling establishment, and drug use may have occurred prior to entering this establishment. Therefore, we are unaware of how substance use may have differentially affected our participants' responding across the two contexts. Richards, Zhang, Mitchell, and de Wit (1999) reported, however, that alcohol consumption did not affect responding on the hypothetical money choice task in a laboratory context. We were also not aware of, nor did we control for, the amount of time the participant was in the gambling establishment or the number of winning or losing wagers that had been made before completing our experiment. This latter point begs the question regarding the mechanism responsible for behavior change across contexts. Relevant variables in the gambling context might include the presence of others who are gambling, alcohol consumption, and the amount of money available to participants. It may have also been the case that the nongambling context was less natural or social in nature than the off-track betting facility. The specific variables that contributed to the between-context differences observed in the present study are unknown, but it seems safe to conclude that a gambling context contains critical variables that alter delay discounting, at least for pathological gamblers.

Future researchers may wish to further explore various additional parameters such as immediate financial instability, which may alter pathological gamblers' discounting. Pietras and Hackenberg (2001), for example, have demonstrated that income and budgetary constraints affect risky choice in humans in the laboratory. In translating the implications of their work to gambling, an experimenter might assess how moment-by-moment wins or losses alter the degree to which that person discounts delayed rewards prior to their initiation of the next wager. Brief discounting tasks could be completed between successive gambles, and comparisons could be made based on prior winning or losing wagers. Additional research might also attempt to evaluate the correspondence between discounting and the actual size of the next wager made by a pathological gambler in a gambling context. Finally, researchers might investigate the potential relations that may exist between gambling severity (as reported using metrics like the SOGS) and degrees of discounting. It may be possible that regression models that include factors such as SOGS score, context, age of onset of disorder, and current indebtedness may be predictive of delay discounting.

In summary, the present experiment illustrates a clear rationale for conducting translational research on delay discounting. The context in which the experimental procedures were conducted altered the choice patterns for many of the participants. There is a growing literature on temporal discounting in people with impulse control disorders. To the extent that insensitivity to delayed or diffuse consequences contributes to the provenance and maintenance of these behavioral problems, understanding the variables that control temporal discounting is of critical importance to the development of effective treatments (see, e.g., Petry, 2005). Identifying the conditions under which an individual is most sensitive to the long-term consequences of his or her behavior may enhance the likelihood that he or she will commit to a course of action that will bring behavior under control of those extended outcomes. Behavior analysts are uniquely poised to advance this research by examining environment-based controlling variables instead of accepting prescientific, organism-based explanations for these pervasive and socially significant behavioral problems.