Skip to main content
PMC home page
Journal of the Experimental Analysis of Behavior logoLink to Journal of the Experimental Analysis of Behavior
. 1990 Jan;53(1):189–200. doi: 10.1901/jeab.1990.53-189

Unification of models for choice between delayed reinforcers.

P R Killeen 1, E Fantino 1
PMCID: PMC1323034  PMID: 2299288

Abstract

Two models for choice between delayed reinforcers, Fantino's delay-reduction theory and Killeen's incentive theory, are reviewed. Incentive theory is amended to incorporate the effects of arousal on alternate types of behavior that might block the reinforcement of the target behavior. This amended version is shown to differ from the delay-reduction theory in a term that is an exponential in incentive theory and a difference in delay-reduction theory. A power series approximation to the exponential generates a model that is formally identical with delay-reduction theory. Correlations between delay-reduction theory and the amended incentive theory show excellent congruence over a range of experimental conditions. Although the assumptions that gave rise to delay-reduction theory and incentive theory remain different and testable, the models deriving from the theories are unlikely to be discriminable by parametric experimental tests. This congruence of the models is recognized by naming the common model the delayed reinforcement model, which is then compared with other models of choice such as Killeen and Fetterman's (1988) behavioral theory of timing, Mazur's (1984) equivalence rule, and Vaughan's (1985) melioration theory.

Full text

PDF
190

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Abarca N., Fantino E. Choice and foraging. J Exp Anal Behav. 1982 Sep;38(2):117–123. doi: 10.1901/jeab.1982.38-117. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Case D. A., Fantino E. The delay-reduction hypothesis of conditioned reinforcement and punishment: Observing behavior. J Exp Anal Behav. 1981 Jan;35(1):93–108. doi: 10.1901/jeab.1981.35-93. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Catania A. C., Sagvolden T., Keller K. J. Reinforcement schedules: Retroactive and proactive effects of reinforcers inserted into fixed-interval performances. J Exp Anal Behav. 1988 Jan;49(1):49–73. doi: 10.1901/jeab.1988.49-49. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Chung S. H. Effects of delayed reinforcement in a concurrent situation. J Exp Anal Behav. 1965 Nov;8(6):439–444. doi: 10.1901/jeab.1965.8-439. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Chung S. H., Herrnstein R. J. Choice and delay of reinforcement. J Exp Anal Behav. 1967 Jan;10(1):67–74. doi: 10.1901/jeab.1967.10-67. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Cicerone R. A. Preference for mixed versus constant delay of reinforcement. J Exp Anal Behav. 1976 Mar;25(2):257–261. doi: 10.1901/jeab.1976.25-257. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Davison M. C. Preference for mixed-interval versus fixed-interval schedules. J Exp Anal Behav. 1969 Mar;12(2):247–252. doi: 10.1901/jeab.1969.12-247. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Davison M. C., Temple W. Preference for fixed-interval schedules: an alternative model. J Exp Anal Behav. 1973 Nov;20(3):393–403. doi: 10.1901/jeab.1973.20-393. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Duncan B., Fantino E. Choice for periodic schedules of reinforcement. J Exp Anal Behav. 1970 Jul;14(1):73–86. doi: 10.1901/jeab.1970.14-73. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Dunn R., Fantino E. Choice and the relative immediacy of reinforcement. J Exp Anal Behav. 1982 Nov;38(3):321–326. doi: 10.1901/jeab.1982.38-321. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Dunn R., Williams B., Royalty P. Devaluation of stimuli contingent on choice: evidence for conditioned reinforcement. J Exp Anal Behav. 1987 Jul;48(1):117–131. doi: 10.1901/jeab.1987.48-117. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Fantino E., Case D. A. Human observing: Maintained by stimuli correlated with reinforcement but not extinction. J Exp Anal Behav. 1983 Sep;40(2):193–210. doi: 10.1901/jeab.1983.40-193. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. Fantino E. Choice and rate of reinforcement. J Exp Anal Behav. 1969 Sep;12(5):723–730. doi: 10.1901/jeab.1969.12-723. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Fantino E., Davison M. Choice: Some quantitative relations. J Exp Anal Behav. 1983 Jul;40(1):1–13. doi: 10.1901/jeab.1983.40-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Fantino E., Preston R. A. Choice and foraging: the effects of accessibility on acceptability. J Exp Anal Behav. 1988 Nov;50(3):395–403. doi: 10.1901/jeab.1988.50-395. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Gentry G. D., Marr M. J. Choice and reinforcement delay. J Exp Anal Behav. 1980 Jan;33(1):27–37. doi: 10.1901/jeab.1980.33-27. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. HERRNSTEIN R. J. SECONDARY REINFORCEMENT AND RATE OF PRIMARY REINFORCEMENT. J Exp Anal Behav. 1964 Jan;7:27–36. doi: 10.1901/jeab.1964.7-27. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Herrnstein R. J. On the law of effect. J Exp Anal Behav. 1970 Mar;13(2):243–266. doi: 10.1901/jeab.1970.13-243. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Hursh S. R. Economic concepts for the analysis of behavior. J Exp Anal Behav. 1980 Sep;34(2):219–238. doi: 10.1901/jeab.1980.34-219. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Hursh S. R., Fantino E. Relative delay of reinforcement and choice. J Exp Anal Behav. 1973 May;19(3):437–450. doi: 10.1901/jeab.1973.19-437. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Ito M., Asaki K. Choice behavior of rats in a concurrent-chains schedule: Amount and delay of reinforcement. J Exp Anal Behav. 1982 May;37(3):383–392. doi: 10.1901/jeab.1982.37-383. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Killeen P. R., Fetterman J. G. A behavioral theory of timing. Psychol Rev. 1988 Apr;95(2):274–295. doi: 10.1037/0033-295x.95.2.274. [DOI] [PubMed] [Google Scholar]
  23. Killeen P. R., Hanson S. J., Osborne S. R. Arousal: its genesis and manifestation as response rate. Psychol Rev. 1978 Nov;85(6):571–581. [PubMed] [Google Scholar]
  24. Killeen P. R. Incentive theory: II. Models for choice. J Exp Anal Behav. 1982 Sep;38(2):217–232. doi: 10.1901/jeab.1982.38-217. [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. Killeen P. On the measurement of reinforcement frequency in the study of preference. J Exp Anal Behav. 1968 May;11(3):263–269. doi: 10.1901/jeab.1968.11-263. [DOI] [PMC free article] [PubMed] [Google Scholar]
  26. Killeen P. Preference for fixed-interval schedules of reinforcement. J Exp Anal Behav. 1970 Sep;14(2):127–131. doi: 10.1901/jeab.1970.14-127. [DOI] [PMC free article] [PubMed] [Google Scholar]
  27. LaFiette M. H., Fantino E. Responding on concurrent-chains schedules in open and closed economies. J Exp Anal Behav. 1989 May;51(3):329–342. doi: 10.1901/jeab.1989.51-329. [DOI] [PMC free article] [PubMed] [Google Scholar]
  28. Macewen D. The effects of terminal-link fixed-interval and variable-interval schedules on responding under concurrent chained schedules. J Exp Anal Behav. 1972 Sep;18(2):253–261. doi: 10.1901/jeab.1972.18-253. [DOI] [PMC free article] [PubMed] [Google Scholar]
  29. Myerson J., Hale S. Choice in transition: A comparison of melioration and the kinetic model. J Exp Anal Behav. 1988 Mar;49(2):291–302. doi: 10.1901/jeab.1988.49-291. [DOI] [PMC free article] [PubMed] [Google Scholar]
  30. Squires N., Fantino E. A model for choice in simple concurrent and concurrent-chains schedules. J Exp Anal Behav. 1971 Jan;15(1):27–38. doi: 10.1901/jeab.1971.15-27. [DOI] [PMC free article] [PubMed] [Google Scholar]
  31. Staddon J. E. Quasi-dynamic choice models: Melioration and ratio invariance. J Exp Anal Behav. 1988 Mar;49(2):303–320. doi: 10.1901/jeab.1988.49-303. [DOI] [PMC free article] [PubMed] [Google Scholar]
  32. Vaughan W. Choice: A local analysis. J Exp Anal Behav. 1985 May;43(3):383–405. doi: 10.1901/jeab.1985.43-383. [DOI] [PMC free article] [PubMed] [Google Scholar]
  33. Williams B. A., Fantino E. Effects on choice of reinforcement delay and conditioned reinforcement. J Exp Anal Behav. 1978 Jan;29(1):77–86. doi: 10.1901/jeab.1978.29-77. [DOI] [PMC free article] [PubMed] [Google Scholar]
  34. Wixted J. T. Nonhuman short-term memory: A quantitative reanalysis of selected findings. J Exp Anal Behav. 1989 Nov;52(3):409–426. doi: 10.1901/jeab.1989.52-409. [DOI] [PMC free article] [PubMed] [Google Scholar]

Articles from Journal of the Experimental Analysis of Behavior are provided here courtesy of Society for the Experimental Analysis of Behavior

RESOURCES