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Delay discounting: Pigeon, rat, human--does it matter? - PubMed

Review

Delay discounting: Pigeon, rat, human--does it matter?

Ariana Vanderveldt et al. J Exp Psychol Anim Learn Cogn. 2016 Apr.

Abstract

Delay discounting refers to the decrease in subjective value of an outcome as the time to its receipt increases. Across species and situations, animals discount delayed rewards, and their discounting is well-described by a hyperboloid function. The current review begins with a comparison of discounting models and the procedures used to assess delay discounting in nonhuman animals. We next discuss the generality of discounting, reviewing the effects of different variables on the degree of discounting delayed reinforcers by nonhuman animals. Despite the many similarities in discounting observed between human and nonhuman animals, several differences have been proposed (e.g., the magnitude effect; nonhuman animals discount over a matter of seconds whereas humans report willing to wait months, if not years before receiving a reward), raising the possibility of fundamental species differences in intertemporal choice. After evaluating these differences, we discuss delay discounting from an adaptationist perspective. The pervasiveness of discounting across species and situations suggests it is a fundamental process underlying decision making.

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Figures

Figure 1
Figure 1

Changes in subjective value of a smaller-sooner (SS) reward and a larger-later (LL) reward. The heights of the bars represent the nominal (i.e., undiscounted) amount of reward. The curves show how subjective values change as a function of delay to the rewards according to the hyperbolic model of discounting (Equation 2). The point at which the two curves intersect indicates the point of preference reversal from LL at T1 to SS at T2.

Figure 2
Figure 2

Percent choice of a smaller, sooner reinforcer as a function of the delay until its receipt. Preference for the smaller, sooner reinforcer increased as time to its receipt approached. The top panel shows percent choice of a smaller, sooner food reinforcer by individual pigeons; the bottom panel shows the mean percent choice by rats of a smaller, sooner food (filled circles) and water (open triangles) reinforcer. Data are from “Preference reversal and self control: Choice as a function of reward amount and delay” by L. Green, E. B., Fisher, S. Perlow, and L. Sherman, 1981, Behaviour Analysis Letters, 1, pp. 43–51, and from “Preference reversals with food and water reinforcers in rats” by L. Green and S. J. Estle, 2003, Journal of the Experimental Analysis of Behavior, 5, pp. 233–242.

Figure 3
Figure 3

Fits of the exponential (Eq. 1), simple hyperbola (Eq. 2), and hyperboloid (Eq. 3) functions to the discounting of a delayed hypothetical $10,000 reward. Data are from “Discounting of delayed rewards: A life-span comparison” by L. Green, A. Fry, and J. Myerson, 1994, Psychological Science, 5, p. 35.

Figure 4
Figure 4

Individual estimates of k for the adjusting-amount procedure plotted against the individual estimates for the corresponding adjusting-delay procedure from both Experiment 1 (filled circles) and Experiment 2 (open circles) of Green et al. (2007). The dashed line represents equivalent rates of discounting. Figure is from “Do adjusting-amount and adjusting-delay procedures produce equivalent estimates of subjective value in pigeons?” by L. Green, J. Myerson, A. K. Shah, S. J. Estle, and D. D. Holt, 2007, Journal of the Experimental Analysis of Behavior, 87, p. 345. Copyright 2007 by John Wiley & Sons, Inc.

Figure 5
Figure 5

Mean percentage choice of the larger reinforcer as a function of the delay to the reinforcer. Filled circles represent choice by rats after orbital prefrontal cortex (OPFC) lesion, and open circles represent choice by the sham lesion control rats. (Error bars show one standard error of the mean.) The dotted horizontal line represents the indifference point, at which the smaller, sooner and the larger, later reinforcers each are chosen 50% of the time. Figure is adapted from “Effects of lesions of the orbitofrontal cortex on sensitivity to delayed and probabilistic reinforcement” by S. Mobini, S. Body, M.-Y. Ho, C. Bradshaw, E Szabadi, J. Deakin, and I Anderson, 2002, Psychopharmacology, 160, p. 292. Copyright 2002 by Springer.

Figure 6
Figure 6

Relative subjective value as a function of delay to receipt of a reward. The top panel shows the discounting of two monetary rewards and the bottom panel shows the discounting of two real liquid rewards of different amounts. In each panel, the larger delayed amount is discounted statistically significantly less steeply as a function of time to its receipt than the smaller, delayed amount (a magnitude effect). Data are from Experiment 2 of “Amount of reward has opposite effects on the discounting of delayed and probabilistic outcomes,” by L. Green, J. Myerson, and P. Ostaszewski, 1999, Journal of Experimental Psychology: Learning, Memory, and Cognition, 25, pp. 418–427, and Experiment 3 of “Are people really more patient than other animals? Evidence from human discounting of real liquid rewards,” by K. Jimura, J. Myerson, J. Hilgard, T. S. Braver, and L. Green, 2009, Psychonomic Bulletin & Review, 16, pp. 1071–1075.

Figure 7
Figure 7

Difference in the discounting rate parameter (k) between smaller and larger delayed amounts in individual rats (dark triangles) and pigeons (grey circles) across four studies using an adjusting-amount procedure. Data are from “Determination of discount functions in rats with an adjusting-amount procedure” by J. B. Richards, S. H. Mitchell, H. de Wit, and L. S. Seiden, 1997, Journal of the Experimental Analysis of Behavior, 67, pp. 353–366, “Discounting of delayed food rewards in pigeons and rats: Is there a magnitude effect?” by L. Green, J. Myerson, D. D. Holt, J. R. Slevin, and S. J. Estle, 2004, Journal of the Experimental Analysis of Behavior, 81, pp. 39–50, “Delay discounting of qualitatively different reinforcers in rats” by A. L. Calvert, L. Green, and J. Myerson, 2010, Journal of the Experimental Analysis of Behavior, 93, pp. 171–184, and “Pigeons’ delay discounting functions established using a concurrent-chains procedure” by L. Oliveira, L. Green, and J. Myerson, 2014, Journal of the Experimental Analysis of Behavior, 102, pp. 151–161.

Figure 8
Figure 8

Obtained subjective values and the best-fitting hyperbolic curves (Eq. 1) as a function of the delay unique to the delivery of the larger, delayed reward. Each curve represents a different common delay condition (i.e., the delay common to the smaller, sooner and the larger, later rewards). The left panel shows the mean subjective value of a $200 reward discounted by humans, and the right panel shows the mean subjective value of a 30-pellet reinforcer discounted by pigeons. Data are from Experiment 1 of “Temporal discounting when the choice is between two delayed rewards,” by L. Green, J. Myerson, and E. W. Macaux, 2005, Journal of Experimental Psychology: Learning, Memory, and Cognition, 31, 1121–1133 and Experiment 2 of “Discounting in pigeons when the choice is between two delayed rewards: Implications for species comparisons,” by A. L. Calvert, L. Green, and J. Myerson, 2011, Frontiers in Neuroscience, 5, 1–10.

Figure 9
Figure 9

Delay (in seconds) at the point of indifference as a function of species’ body mass. Greater delays indicate shallower discounting. (Note that the axes are logarithmically scaled.) Figure is adapted from “Intertemporal choice in lemurs”, by J. R. Stevens and N. Mühlhoff, 2012, Behavioural Processes, 89, p. 126. Copyright 2012 by Elsevier.

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