Discounting of probabilistic food reinforcement by pigeons.

Bibliographic Details
Title: Discounting of probabilistic food reinforcement by pigeons.
Authors: Oliveira L; Department of Psychological & Brain Sciences, Washington University, St. Louis, MO, USA., Green L; Department of Psychological & Brain Sciences, Washington University, St. Louis, MO, USA., Myerson J; Department of Psychological & Brain Sciences, Washington University, St. Louis, MO, USA., Wan H; Department of Psychological & Brain Sciences, Washington University, St. Louis, MO, USA.
Source: Journal of the experimental analysis of behavior [J Exp Anal Behav] 2025 Jul; Vol. 124 (1), pp. e70042.
Publication Type: Journal Article
Language: English
Journal Info: Publisher: Wiley-Blackwell Country of Publication: United States NLM ID: 0203727 Publication Model: Print Cited Medium: Internet ISSN: 1938-3711 (Electronic) Linking ISSN: 00225002 NLM ISO Abbreviation: J Exp Anal Behav Subsets: MEDLINE
Imprint Name(s): Publication: [Malden, MA] : Wiley-Blackwell
Original Publication: Waltham, Mass., Society for the Experimental Analysis of Behavior.
MeSH Terms: Delay Discounting* , Reinforcement, Psychology* , Choice Behavior* , Probability Learning*, Animals ; Columbidae ; Conditioning, Operant ; Reinforcement Schedule ; Food ; Probability
Abstract: Two experiments examined pigeons' discounting of probabilistic food reinforcers using a concurrent-chains procedure within sessions combined with an adjusting-amount procedure across sessions. The study is the first to evaluate probability discounting functions in nonhuman animals in which the obtained probability equaled that programmed in each session. In Experiment 1, pigeons chose between a smaller, certain and a larger, but probabilistic food reinforcer. In Experiment 2, the probabilities of receiving both reinforcement options were reduced by a common factor, creating a choice situation in which both options were probabilistic: a smaller, more probable reinforcer and a larger, but less probable reinforcer. Results revealed that regardless of whether choices involved a certain versus a probabilistic reinforcer or they involved two probabilistic reinforcers, subjective value decreased systematically as a function of the odds against receipt of the reinforcer and that the data were well described by the hyperboloid discounting function. In addition, no significant effect of reinforcer amount on degree of probability discounting was observed, consistent with results from studies of the discounting of delayed reinforcers by nonhuman animals.
(© 2025 Society for the Experimental Analysis of Behavior.)
References: Alsop, B., & Davison, M. (1986). Preference for multiple versus mixed schedules of reinforcement. Journal of the Experimental Analysis of Behavior, 45(1), 33–45. https://doi.org/10.1901/jeab.1986.45-33.
Autor, S. M. (1969). The strength of conditioned reinforcers as a function of frequency and probability of reinforcement. In D. Hendry (Ed.), Conditioned reinforcement (pp. 127–162). Dorsey Press.
Baker, F., Johnson, M. W., & Bickel, W. K. (2003). Delay discounting in current and never‐before cigarette smokers: Similarities and differences across commodity, sign, and magnitude. Journal of Abnormal Psychology, 112(3), 382–392. https://doi.org/10.1037/0021-843X.112.3.382.
Bickel, W. K., Odum, A. L., & Madden, G. J. (1999). Impulsivity and cigarette smoking: Delay discounting in current, never, and ex‐smokers. Psychopharmacology, 146(4), 447–454. https://doi.org/10.1007/PL00005490.
Bodeker, R. R. H., & Grace, R. C. (2024a). Effects of methamphetamine on delay discounting in rats using concurrent chains. Learning & Behavior. https://doi.org/10.3758/s13420-024-00657-w.
Bodeker, R. R. H., & Grace, R. C. (2024b). Effects of methamphetamine on probability discounting in rats using concurrent chains. Behavioural Processes, 214, Article 104971. https://doi.org/10.1016/j.beproc.2023.104971.
Brown, P. L., & Jenkins, H. M. (1968). Auto‐shaping of the pigeon's key‐peck. Journal of the Experimental Analysis of Behavior, 11(1), 1–8. https://doi.org/10.1901/jeab.1968.11-1.
Bürkner, P.‐C. (2017). brms: An R package for Bayesian multilevel models using Stan. Journal of Statistical Software, 80(1), 1–28. https://doi.org/10.18637/jss.v080.i01.
Calvert, A. L., Green, L., & Myerson, J. (2010). Delay discounting of qualitatively different reinforcers in rats. Journal of the Experimental Analysis of Behavior, 93(2), 171–184. https://doi.org/10.1901/jeab.2010.93-171.
Caraco, T., Martindale, S., & Whittam, T. S. (1980). An empirical demonstration of risk‐sensitive foraging preferences. Animal Behaviour, 28(3), 820–830. https://doi.org/10.1016/S0003-3472(80)80142-4.
Carpenter, B., Gelman, A., Hoffman, M. D., Lee, D., Goodrich, B., Betancourt, M., Brubaker, M. A., Guo, J., Li, P., & Riddell, A. (2017). Stan: A probabilistic programming language. Journal of Statistical Software, 76, Article 1. 10.18637/jss.v076.i01.
Davison, M., & Jenkins, P. E. (1985). Stimulus discriminability, contingency discriminability, and schedule performance. Animal Learning & Behavior, 13(1), 77–84. https://doi.org/10.3758/BF03213368.
Douma, J. C., & Weedon, J. T. (2019). Analysing continuous proportions in ecology and evolution: A practical introduction to beta and Dirichlet regression. Methods in Ecology and Evolution, 10(9), 1412–1430. https://doi.org/10.1111/2041-210X.13234.
Du, W., Green, L., & Myerson, J. (2002). Cross‐cultural comparisons of discounting delayed and probabilistic rewards. The Psychological Record, 52(4), 479–492. https://doi.org/10.1007/BF03395199.
Estle, S. J., Green, L., Myerson, J., & Holt, D. D. (2006). Differential effects of amount on temporal and probability discounting of gains and losses. Memory & Cognition, 34(4), 914–928. https://doi.org/10.3758/BF03193437.
Fleshler, M., & Hoffman, H. S. (1962). A progression for generating variable‐interval schedules. Journal of the Experimental Analysis of Behavior, 5(4), 529–530. https://doi.org/10.1901/jeab.1962.5-529.
Freeman, K. B., Nonnemacher, J. E., Green, L., Myerson, J., & Woolverton, W. L. (2012). Delay discounting in rhesus monkeys: Equivalent discounting of more and less preferred sucrose concentrations. Learning & Behavior, 40(1), 54–60. https://doi.org/10.3758/s13420-011-0045-3.
Gabry, J., & Češnovar, R. (2022). cmdstanr: R interface to CmdStan [Computer software]. https://mc-stan.org/cmdstanr/.
Grace, R. C., & McLean, A. P. (2015). Evidence for a magnitude effect in probability discounting with pigeons. Journal of Experimental Psychology: Animal Learning and Cognition, 41(4), 406–418. https://doi.org/10.1037/xan0000077.
Grace, R. C., Sargisson, R. J., & White, K. G. (2012). Evidence for a magnitude effect in temporal discounting with pigeons. Journal of Experimental Psychology: Animal Behavior Processes, 38(1), 102–108. https://doi.org/10.1037/a0026345.
Green, L., & Myerson, J. (2004). A discounting framework for choice with delayed and probabilistic rewards. Psychological Bulletin, 130(5), 769–792. https://doi.org/10.1037/0033-2909.130.5.769.
Green, L., Myerson, J., & Calvert, A. L. (2010). Pigeons' discounting of probabilistic and delayed reinforcers. Journal of the Experimental Analysis of Behavior, 94(2), 113–123. https://doi.org/10.1901/jeab.2010.94-113.
Green, L., Myerson, J., Holt, D. D., Slevin, J. R., & Estle, S. J. (2004). Discounting of delayed food rewards in pigeons and rats: Is there a magnitude effect? Journal of the Experimental Analysis of Behavior, 81(1), 39–50. https://doi.org/10.1901/jeab.2004.81-39.
Green, L., Myerson, J., Oliveira, L., & Chang, S. E. (2013). Delay discounting of monetary rewards over a wide range of amounts. Journal of the Experimental Analysis of Behavior, 100(3), 269–281. https://doi.org/10.1002/jeab.45.
Green, L., Myerson, J., Shah, A. K., Estle, S. J., & Holt, D. D. (2007). Do adjusting‐amount and adjusting‐delay procedures produce equivalent estimates of subjective value in pigeons? Journal of the Experimental Analysis of Behavior, 87(3), 337–347. https://doi.org/10.1901/jeab.2007.37-06.
Green, L., Myerson, J., & Vanderveldt, A. (2014). Delay and probability discounting. In F. K. McSweeney & E. S. Murphy (Eds.), The Wiley Blackwell handbook of operant and classical conditioning (pp. 307–337). Wiley. https://doi.org/10.1002/9781118468135.ch13.
Herrnstein, R. J. (1970). On the law of effect. Journal of the Experimental Analysis of Behavior, 13(2), 243–266. https://doi.org/10.1901/jeab.1970.13-243.
Holt, D. D., Green, L., & Myerson, J. (2003). Is discounting impulsive? Evidence from temporal and probability discounting in gambling and non‐gambling college students. Behavioural Processes, 64(3), 355–367. https://doi.org/10.1016/S0376-6357(03)00141-4.
Johnson, M. W., & Bickel, W. K. (2002). Within‐subject comparison of real and hypothetical money rewards in delay discounting. Journal of the Experimental Analysis of Behavior, 77(2), 129–146. https://doi.org/10.1901/jeab.2002.77-129.
Johnson, M. W., Strickland, J. C., Herrmann, E. S., Dolan, S. B., Cox, D. J., & Berry, M. S. (2021). Sexual discounting: A systematic review of discounting processes and sexual behavior. Experimental and Clinical Psychopharmacology, 29(6), 711–738. https://doi.org/10.1037/pha0000402.
Jones, B. A., & Rachlin, H. (2009). Delay, probability, and social discounting in a public goods game. Journal of the Experimental Analysis of Behavior, 91(1), 61–73. https://doi.org/10.1901/jeab.2009.91-61.
Madden, G. J., Begotka, A. M., Raiff, B. R., & Kastern, L. L. (2003). Delay discounting of real and hypothetical rewards. Experimental and Clinical Psychopharmacology, 11(2), 139–145. https://doi.org/10.1037/1064-1297.11.2.139.
Madden, G. J., Raiff, B. R., Lagorio, C. H., Begotka, A. M., Mueller, A. M., Hehli, D. J., & Wegener, A. A. (2004). Delay discounting of potentially real and hypothetical rewards: II. between‐ and within‐subject comparisons. Experimental and Clinical Psychopharmacology, 12(4), 251–261. https://doi.org/10.1037/1064-1297.12.4.251.
McKerchar, T. L., Green, L., & Myerson, J. (2010). On the scaling interpretation of exponents in hyperboloid models of delay and probability discounting. Behavioural Processes, 84(1), 440–444. https://doi.org/10.1016/j.beproc.2010.01.003.
McNamara, J. M., & Houston, A. I. (1992). Risk‐sensitive foraging: A review of the theory. Bulletin of Mathematical Biology, 54(2–3), 355–378. https://doi.org/10.1007/BF02464838.
Mejía‐Cruz, D., Green, L., Myerson, J., Morales‐Chainé, S., & Nieto, J. (2016). Delay and probability discounting by drug‐dependent cocaine and marijuana users. Psychopharmacology, 233(14), 2705–2714. https://doi.org/10.1007/s00213-016-4316-8.
Mobini, S., Body, S., Ho, M.‐Y., Bradshaw, C., Szabadi, E., Deakin, J., & Anderson, I. (2002). Effects of lesions of the orbitofrontal cortex on sensitivity to delayed and probabilistic reinforcement. Psychopharmacology, 160(3), 290–298. https://doi.org/10.1007/s00213-001-0983-0.
Mobini, S., Chiang, T.‐J., Ho, M.‐Y., Bradshaw, C. M., & Szabadi, E. (2000). Effects of central 5‐hydroxytryptamine depletion on sensitivity to delayed and probabilistic reinforcement. Psychopharmacology, 152(4), 390–397. https://doi.org/10.1007/s002130000542.
Myerson, J., & Green, L. (1995). Discounting of delayed rewards: Models of individual choice. Journal of the Experimental Analysis of Behavior, 64(3), 263–276. https://doi.org/10.1901/jeab.1995.64-263.
Myerson, J., Green, L., & Morris, J. (2011). Modeling the effect of reward amount on probability discounting. Journal of the Experimental Analysis of Behavior, 95(2), 175–187. https://doi.org/10.1901/jeab.2011.95-175.
Myerson, J., Green, L., & Warusawitharana, M. (2001). Area under the curve as a measure of discounting. Journal of the Experimental Analysis of Behavior, 76(2), 235–243. https://doi.org/10.1901/jeab.2001.76-235.
Oliveira, L., Green, L., & Myerson, J. (2014). Pigeons' delay discounting functions established using a concurrent‐chains procedure. Journal of the Experimental Analysis of Behavior, 102(2), 151–161. https://doi.org/10.1002/jeab.97.
R Core Team. (2022). R: A language and environment for statistical computing [Computer software]. R Foundation for Statistical Computing. https://www.R-project.org/.
Rachlin, H. (2006). Notes on discounting. Journal of the Experimental Analysis of Behavior, 85(3), 425–435. https://doi.org/10.1901/jeab.2006.85-05.
Rachlin, H., Brown, J., & Cross, D. (2000). Discounting in judgments of delay and probability. Journal of Behavioral Decision Making, 13(2), 145–159. https://doi.org/10.1002/(SICI)1099‐0771(200004/06)13:2<145::AID‐BDM320>3.0.CO;2‐4.
Raineri, A., & Rachlin, H. (1993). The effect of temporal constraints on the value of money and other commodities. Journal of Behavioral Decision Making, 6(2), 77–94. https://doi.org/10.1002/bdm.3960060202.
Richards, J. B., Mitchell, S. H., De Wit, H., & Seiden, L. S. (1997). Determination of discount functions in rats with an adjusting‐amount procedure. Journal of the Experimental Analysis of Behavior, 67(3), 353–366. https://doi.org/10.1901/jeab.1997.67-353.
Shahan, T. A., & Lattal, K. A. (1998). On the functions of the changeover delay. Journal of the Experimental Analysis of Behavior, 69(2), 141–160. https://doi.org/10.1901/jeab.1998.69-141.
Stephens, D. W., & Charnov, E. L. (1982). Optimal foraging: Some simple stochastic models. Behavioral Ecology and Sociobiology, 10(4), 251–263. https://doi.org/10.1007/BF00302814.
Stubbs, D. A., & Pliskoff, S. S. (1969). Concurrent responding with fixed relative rate of reinforcement. Journal of the Experimental Analysis of Behavior, 12(6), 887–895. https://doi.org/10.1901/jeab.1969.12-887.
Vanderveldt, A., Oliveira, L., & Green, L. (2016). Delay discounting: Pigeon, rat, human—does it matter? Journal of Experimental Psychology: Animal Learning and Cognition, 42(2), 141–162. https://doi.org/10.1037/xan0000097.
Wan, H., Myerson, J., & Green, L. (2023). Individual differences in degree of discounting: Do different procedures and measures assess the same construct? Behavioural Processes, 208, Article 104864. https://doi.org/10.1016/j.beproc.2023.104864.
Wan, H., Myerson, J., Green, L., Strube, M. J., & Hale, S. (2024). Age‐related differences in delay discounting: Income matters. Psychology and Aging, 39(6), 632–643. https://doi.org/10.1037/pag0000818.
Wilhelm, C. J., & Mitchell, S. H. (2008). Rats bred for high alcohol drinking are more sensitive to delayed and probabilistic outcomes. Genes, Brain and Behavior, 7(7), 705–713. https://doi.org/10.1111/j.1601-183X.2008.00406.x.
Grant Information: RO1 MH055308 United States NH NIH HHS
Contributed Indexing: Keywords: adjusting amount; concurrent chains; hyperboloid; pigeon; probability discounting
Entry Date(s): Date Created: 20250715 Date Completed: 20250715 Latest Revision: 20250715
Update Code: 20260130
DOI: 10.1002/jeab.70042
PMID: 40662635
Database: MEDLINE
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  Data: Two experiments examined pigeons&#39; discounting of probabilistic food reinforcers using a concurrent-chains procedure within sessions combined with an adjusting-amount procedure across sessions. The study is the first to evaluate probability discounting functions in nonhuman animals in which the obtained probability equaled that programmed in each session. In Experiment 1, pigeons chose between a smaller, certain and a larger, but probabilistic food reinforcer. In Experiment 2, the probabilities of receiving both reinforcement options were reduced by a common factor, creating a choice situation in which both options were probabilistic: a smaller, more probable reinforcer and a larger, but less probable reinforcer. Results revealed that regardless of whether choices involved a certain versus a probabilistic reinforcer or they involved two probabilistic reinforcers, subjective value decreased systematically as a function of the odds against receipt of the reinforcer and that the data were well described by the hyperboloid discounting function. In addition, no significant effect of reinforcer amount on degree of probability discounting was observed, consistent with results from studies of the discounting of delayed reinforcers by nonhuman animals.&lt;br /&gt; (&#169; 2025 Society for the Experimental Analysis of Behavior.)
– Name: Ref
  Label: References
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  Data: Alsop, B., &amp; Davison, M. (1986). Preference for multiple versus mixed schedules of reinforcement. Journal of the Experimental Analysis of Behavior, 45(1), 33–45. https://doi.org/10.1901/jeab.1986.45-33.&lt;br /&gt;Autor, S. M. (1969). The strength of conditioned reinforcers as a function of frequency and probability of reinforcement. In D. Hendry (Ed.), Conditioned reinforcement (pp. 127–162). Dorsey Press.&lt;br /&gt;Baker, F., Johnson, M. W., &amp; Bickel, W. K. (2003). Delay discounting in current and never‐before cigarette smokers: Similarities and differences across commodity, sign, and magnitude. Journal of Abnormal Psychology, 112(3), 382–392. https://doi.org/10.1037/0021-843X.112.3.382.&lt;br /&gt;Bickel, W. K., Odum, A. L., &amp; Madden, G. J. (1999). Impulsivity and cigarette smoking: Delay discounting in current, never, and ex‐smokers. Psychopharmacology, 146(4), 447–454. https://doi.org/10.1007/PL00005490.&lt;br /&gt;Bodeker, R. R. H., &amp; Grace, R. C. (2024a). Effects of methamphetamine on delay discounting in rats using concurrent chains. Learning &amp; Behavior. https://doi.org/10.3758/s13420-024-00657-w.&lt;br /&gt;Bodeker, R. R. H., &amp; Grace, R. C. (2024b). Effects of methamphetamine on probability discounting in rats using concurrent chains. Behavioural Processes, 214, Article 104971. https://doi.org/10.1016/j.beproc.2023.104971.&lt;br /&gt;Brown, P. L., &amp; Jenkins, H. M. (1968). Auto‐shaping of the pigeon&#39;s key‐peck. Journal of the Experimental Analysis of Behavior, 11(1), 1–8. https://doi.org/10.1901/jeab.1968.11-1.&lt;br /&gt;B&#252;rkner, P.‐C. (2017). brms: An R package for Bayesian multilevel models using Stan. Journal of Statistical Software, 80(1), 1–28. https://doi.org/10.18637/jss.v080.i01.&lt;br /&gt;Calvert, A. L., Green, L., &amp; Myerson, J. (2010). Delay discounting of qualitatively different reinforcers in rats. Journal of the Experimental Analysis of Behavior, 93(2), 171–184. https://doi.org/10.1901/jeab.2010.93-171.&lt;br /&gt;Caraco, T., Martindale, S., &amp; Whittam, T. S. (1980). An empirical demonstration of risk‐sensitive foraging preferences. Animal Behaviour, 28(3), 820–830. https://doi.org/10.1016/S0003-3472(80)80142-4.&lt;br /&gt;Carpenter, B., Gelman, A., Hoffman, M. D., Lee, D., Goodrich, B., Betancourt, M., Brubaker, M. A., Guo, J., Li, P., &amp; Riddell, A. (2017). Stan: A probabilistic programming language. Journal of Statistical Software, 76, Article 1. 10.18637/jss.v076.i01.&lt;br /&gt;Davison, M., &amp; Jenkins, P. E. (1985). Stimulus discriminability, contingency discriminability, and schedule performance. Animal Learning &amp; Behavior, 13(1), 77–84. https://doi.org/10.3758/BF03213368.&lt;br /&gt;Douma, J. C., &amp; Weedon, J. T. (2019). Analysing continuous proportions in ecology and evolution: A practical introduction to beta and Dirichlet regression. Methods in Ecology and Evolution, 10(9), 1412–1430. https://doi.org/10.1111/2041-210X.13234.&lt;br /&gt;Du, W., Green, L., &amp; Myerson, J. (2002). Cross‐cultural comparisons of discounting delayed and probabilistic rewards. The Psychological Record, 52(4), 479–492. https://doi.org/10.1007/BF03395199.&lt;br /&gt;Estle, S. J., Green, L., Myerson, J., &amp; Holt, D. D. (2006). Differential effects of amount on temporal and probability discounting of gains and losses. Memory &amp; Cognition, 34(4), 914–928. https://doi.org/10.3758/BF03193437.&lt;br /&gt;Fleshler, M., &amp; Hoffman, H. S. (1962). A progression for generating variable‐interval schedules. Journal of the Experimental Analysis of Behavior, 5(4), 529–530. https://doi.org/10.1901/jeab.1962.5-529.&lt;br /&gt;Freeman, K. B., Nonnemacher, J. E., Green, L., Myerson, J., &amp; Woolverton, W. L. (2012). Delay discounting in rhesus monkeys: Equivalent discounting of more and less preferred sucrose concentrations. Learning &amp; Behavior, 40(1), 54–60. https://doi.org/10.3758/s13420-011-0045-3.&lt;br /&gt;Gabry, J., &amp; Češnovar, R. (2022). cmdstanr: R interface to CmdStan [Computer software]. https://mc-stan.org/cmdstanr/.&lt;br /&gt;Grace, R. C., &amp; McLean, A. P. (2015). Evidence for a magnitude effect in probability discounting with pigeons. Journal of Experimental Psychology: Animal Learning and Cognition, 41(4), 406–418. https://doi.org/10.1037/xan0000077.&lt;br /&gt;Grace, R. C., Sargisson, R. J., &amp; White, K. G. (2012). Evidence for a magnitude effect in temporal discounting with pigeons. Journal of Experimental Psychology: Animal Behavior Processes, 38(1), 102–108. https://doi.org/10.1037/a0026345.&lt;br /&gt;Green, L., &amp; Myerson, J. (2004). A discounting framework for choice with delayed and probabilistic rewards. Psychological Bulletin, 130(5), 769–792. https://doi.org/10.1037/0033-2909.130.5.769.&lt;br /&gt;Green, L., Myerson, J., &amp; Calvert, A. L. (2010). Pigeons&#39; discounting of probabilistic and delayed reinforcers. Journal of the Experimental Analysis of Behavior, 94(2), 113–123. https://doi.org/10.1901/jeab.2010.94-113.&lt;br /&gt;Green, L., Myerson, J., Holt, D. D., Slevin, J. R., &amp; Estle, S. J. (2004). Discounting of delayed food rewards in pigeons and rats: Is there a magnitude effect? Journal of the Experimental Analysis of Behavior, 81(1), 39–50. https://doi.org/10.1901/jeab.2004.81-39.&lt;br /&gt;Green, L., Myerson, J., Oliveira, L., &amp; Chang, S. E. (2013). Delay discounting of monetary rewards over a wide range of amounts. Journal of the Experimental Analysis of Behavior, 100(3), 269–281. https://doi.org/10.1002/jeab.45.&lt;br /&gt;Green, L., Myerson, J., Shah, A. K., Estle, S. J., &amp; Holt, D. D. (2007). Do adjusting‐amount and adjusting‐delay procedures produce equivalent estimates of subjective value in pigeons? Journal of the Experimental Analysis of Behavior, 87(3), 337–347. https://doi.org/10.1901/jeab.2007.37-06.&lt;br /&gt;Green, L., Myerson, J., &amp; Vanderveldt, A. (2014). Delay and probability discounting. In F. K. McSweeney &amp; E. S. Murphy (Eds.), The Wiley Blackwell handbook of operant and classical conditioning (pp. 307–337). Wiley. https://doi.org/10.1002/9781118468135.ch13.&lt;br /&gt;Herrnstein, R. J. (1970). On the law of effect. Journal of the Experimental Analysis of Behavior, 13(2), 243–266. https://doi.org/10.1901/jeab.1970.13-243.&lt;br /&gt;Holt, D. D., Green, L., &amp; Myerson, J. (2003). Is discounting impulsive? Evidence from temporal and probability discounting in gambling and non‐gambling college students. Behavioural Processes, 64(3), 355–367. https://doi.org/10.1016/S0376-6357(03)00141-4.&lt;br /&gt;Johnson, M. W., &amp; Bickel, W. K. (2002). Within‐subject comparison of real and hypothetical money rewards in delay discounting. Journal of the Experimental Analysis of Behavior, 77(2), 129–146. https://doi.org/10.1901/jeab.2002.77-129.&lt;br /&gt;Johnson, M. W., Strickland, J. C., Herrmann, E. S., Dolan, S. B., Cox, D. J., &amp; Berry, M. S. (2021). Sexual discounting: A systematic review of discounting processes and sexual behavior. Experimental and Clinical Psychopharmacology, 29(6), 711–738. https://doi.org/10.1037/pha0000402.&lt;br /&gt;Jones, B. A., &amp; Rachlin, H. (2009). Delay, probability, and social discounting in a public goods game. Journal of the Experimental Analysis of Behavior, 91(1), 61–73. https://doi.org/10.1901/jeab.2009.91-61.&lt;br /&gt;Madden, G. J., Begotka, A. M., Raiff, B. R., &amp; Kastern, L. L. (2003). Delay discounting of real and hypothetical rewards. Experimental and Clinical Psychopharmacology, 11(2), 139–145. https://doi.org/10.1037/1064-1297.11.2.139.&lt;br /&gt;Madden, G. J., Raiff, B. R., Lagorio, C. H., Begotka, A. M., Mueller, A. M., Hehli, D. J., &amp; Wegener, A. A. (2004). Delay discounting of potentially real and hypothetical rewards: II. between‐ and within‐subject comparisons. Experimental and Clinical Psychopharmacology, 12(4), 251–261. https://doi.org/10.1037/1064-1297.12.4.251.&lt;br /&gt;McKerchar, T. L., Green, L., &amp; Myerson, J. (2010). On the scaling interpretation of exponents in hyperboloid models of delay and probability discounting. Behavioural Processes, 84(1), 440–444. https://doi.org/10.1016/j.beproc.2010.01.003.&lt;br /&gt;McNamara, J. M., &amp; Houston, A. I. (1992). Risk‐sensitive foraging: A review of the theory. Bulletin of Mathematical Biology, 54(2–3), 355–378. https://doi.org/10.1007/BF02464838.&lt;br /&gt;Mej&#237;a‐Cruz, D., Green, L., Myerson, J., Morales‐Chain&#233;, S., &amp; Nieto, J. (2016). Delay and probability discounting by drug‐dependent cocaine and marijuana users. Psychopharmacology, 233(14), 2705–2714. https://doi.org/10.1007/s00213-016-4316-8.&lt;br /&gt;Mobini, S., Body, S., Ho, M.‐Y., Bradshaw, C., Szabadi, E., Deakin, J., &amp; Anderson, I. (2002). Effects of lesions of the orbitofrontal cortex on sensitivity to delayed and probabilistic reinforcement. Psychopharmacology, 160(3), 290–298. https://doi.org/10.1007/s00213-001-0983-0.&lt;br /&gt;Mobini, S., Chiang, T.‐J., Ho, M.‐Y., Bradshaw, C. M., &amp; Szabadi, E. (2000). Effects of central 5‐hydroxytryptamine depletion on sensitivity to delayed and probabilistic reinforcement. Psychopharmacology, 152(4), 390–397. https://doi.org/10.1007/s002130000542.&lt;br /&gt;Myerson, J., &amp; Green, L. (1995). Discounting of delayed rewards: Models of individual choice. Journal of the Experimental Analysis of Behavior, 64(3), 263–276. https://doi.org/10.1901/jeab.1995.64-263.&lt;br /&gt;Myerson, J., Green, L., &amp; Morris, J. (2011). Modeling the effect of reward amount on probability discounting. Journal of the Experimental Analysis of Behavior, 95(2), 175–187. https://doi.org/10.1901/jeab.2011.95-175.&lt;br /&gt;Myerson, J., Green, L., &amp; Warusawitharana, M. (2001). Area under the curve as a measure of discounting. Journal of the Experimental Analysis of Behavior, 76(2), 235–243. https://doi.org/10.1901/jeab.2001.76-235.&lt;br /&gt;Oliveira, L., Green, L., &amp; Myerson, J. (2014). Pigeons&#39; delay discounting functions established using a concurrent‐chains procedure. Journal of the Experimental Analysis of Behavior, 102(2), 151–161. https://doi.org/10.1002/jeab.97.&lt;br /&gt;R Core Team. (2022). R: A language and environment for statistical computing [Computer software]. R Foundation for Statistical Computing. https://www.R-project.org/.&lt;br /&gt;Rachlin, H. (2006). Notes on discounting. Journal of the Experimental Analysis of Behavior, 85(3), 425–435. https://doi.org/10.1901/jeab.2006.85-05.&lt;br /&gt;Rachlin, H., Brown, J., &amp; Cross, D. (2000). Discounting in judgments of delay and probability. Journal of Behavioral Decision Making, 13(2), 145–159. https://doi.org/10.1002/(SICI)1099‐0771(200004/06)13:2&amp;lt;145::AID‐BDM320&amp;gt;3.0.CO;2‐4.&lt;br /&gt;Raineri, A., &amp; Rachlin, H. (1993). The effect of temporal constraints on the value of money and other commodities. Journal of Behavioral Decision Making, 6(2), 77–94. https://doi.org/10.1002/bdm.3960060202.&lt;br /&gt;Richards, J. B., Mitchell, S. H., De Wit, H., &amp; Seiden, L. S. (1997). Determination of discount functions in rats with an adjusting‐amount procedure. Journal of the Experimental Analysis of Behavior, 67(3), 353–366. https://doi.org/10.1901/jeab.1997.67-353.&lt;br /&gt;Shahan, T. A., &amp; Lattal, K. A. (1998). On the functions of the changeover delay. Journal of the Experimental Analysis of Behavior, 69(2), 141–160. https://doi.org/10.1901/jeab.1998.69-141.&lt;br /&gt;Stephens, D. W., &amp; Charnov, E. L. (1982). Optimal foraging: Some simple stochastic models. Behavioral Ecology and Sociobiology, 10(4), 251–263. https://doi.org/10.1007/BF00302814.&lt;br /&gt;Stubbs, D. A., &amp; Pliskoff, S. S. (1969). Concurrent responding with fixed relative rate of reinforcement. Journal of the Experimental Analysis of Behavior, 12(6), 887–895. https://doi.org/10.1901/jeab.1969.12-887.&lt;br /&gt;Vanderveldt, A., Oliveira, L., &amp; Green, L. (2016). Delay discounting: Pigeon, rat, human—does it matter? Journal of Experimental Psychology: Animal Learning and Cognition, 42(2), 141–162. https://doi.org/10.1037/xan0000097.&lt;br /&gt;Wan, H., Myerson, J., &amp; Green, L. (2023). Individual differences in degree of discounting: Do different procedures and measures assess the same construct? Behavioural Processes, 208, Article 104864. https://doi.org/10.1016/j.beproc.2023.104864.&lt;br /&gt;Wan, H., Myerson, J., Green, L., Strube, M. J., &amp; Hale, S. (2024). Age‐related differences in delay discounting: Income matters. Psychology and Aging, 39(6), 632–643. https://doi.org/10.1037/pag0000818.&lt;br /&gt;Wilhelm, C. J., &amp; Mitchell, S. H. (2008). Rats bred for high alcohol drinking are more sensitive to delayed and probabilistic outcomes. Genes, Brain and Behavior, 7(7), 705–713. https://doi.org/10.1111/j.1601-183X.2008.00406.x.
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      – SubjectFull: Columbidae
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      – SubjectFull: Reinforcement, Psychology
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      – SubjectFull: Choice Behavior
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      – SubjectFull: Probability Learning
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              Text: 2025 Jul
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