CoChat
Sign Up
Cited by 294Decision-Making and Behavioral EconomicsAnimal Behavior and ReproductionNeural and Behavioral Psychology Studies

Exponential versus hyperbolic discounting of delayed outcomes: Risk and waiting time.

GREEN, LEONARD, MYERSON, JOEL·1996·American Zoologist
DOI 10.1093/icb/36.4.496
Open this paper in CoChat — free account

Abstract

Frequently, animals must choose between more immediate, smaller rewards and more delayed, but larger rewards. For example, they often must decide between accepting a smaller prey item versus continuing to search for a larger one, or between entering a leaner patch versus travelling to a richer patch that is further away. In both situations, choice of the more immediate, but smaller reward may be interpreted as implying that the value of the later reward is discounted; that is, the value of the later reward decreases as the delay to its receipt increases. This decrease in value may occur because of the increased risk involved in waiting for rewards, or because of the decreased rate of reward associated with increased waiting time. The present research attempts to determine the form of the relation between value and delay, and examines implications of this relation for mechanisms underlying risk-sensitive foraging. Two accounts of the relation between value and delay have been proposed to describe the decrease in value resulting from increases in delay: an exponential model and a hyperbolic model. Our research demonstrates that, of the two, a hyperbola-like discounting model consistently explains more of the variance in temporal discounting data at the group level and, importantly, at the individual level as well. We show mathematically that the hyperbolic model shares fundamental features with models of prey and patch choice. In addition, the present review highlights the implications of a psychological perspective for the behavioral biology of risksensitive foraging, as well as the implications of an ecological perspective for the behavioral psychology of risk-sensitive choice and decision-making.

Integrity signals

Registry

Crossref · 10.1093/icb/36.4.496

Cites

22 of 22 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Green et al. (1996) found that for both lower and higher income older adult groups, their discounting data were well described by a hyperbola (Equation 2).

    “Green et al. (1996) observed that for both groups, their data were well described by a hyperbola (Equation 2)”

    From A Discounting Framework for Choice With Delayed and Probabilistic Rewards. (2004) · cites this paper as Green et al. (1996)

  • Lower income older adults discounted delayed rewards much more steeply than higher income older adults.

    “the lower income older adults discounted delayed rewards much more steeply than the higher income older groups.”

    From A Discounting Framework for Choice With Delayed and Probabilistic Rewards. (2004) · cites this paper as Green et al. (1996)

  • Among upper income adults, no age difference in discounting was observed between a younger group (mean age 33 years) and older groups (mean age 71 years).

    “A younger group (mean age = 33 years) of upper income adults was also tested, and no age difference was observed between the two upper income groups.”

    From A Discounting Framework for Choice With Delayed and Probabilistic Rewards. (2004) · cites this paper as Green et al. (1996)

  • Green et al.'s (1996) results run counter to what would be expected on the basis of the effect of amount of reward on rate of discounting.

    “yet Green et al.’s (1996) results run counter to what would be expected on the basis of the effect of amount of reward on rate of discounting.”

    From A Discounting Framework for Choice With Delayed and Probabilistic Rewards. (2004) · cites this paper as Green et al. (1996)

  • Green et al.'s (1996) results suggest that low-income individuals discount a given amount more steeply than high-income individuals, even when education is equivalent.

    “Yet Green et al.’s (1996) results suggest that the opposite is the case, even when the level of education is equivalent in both groups.”

    From A Discounting Framework for Choice With Delayed and Probabilistic Rewards. (2004) · cites this paper as Green et al. (1996)

Cites

Flagged first, then by citations

Cited by

Sorted by citations

Related

Authors
GREEN, L., & MYERSON, J.
Affiliations
Washington University in St. Louis (US)
ORCID
Venue
American Zoologist
Publisher
Oxford University Press (OUP)
Published
1996-09
Volume
36
Issue
4
Pages
496-505
ISSN
0003-1569 (ISSN-L)
DOI
10.1093/icb/36.4.496
OpenAlex
W2084762552
Cited by
294
References
22
Citations by year
2026: 5 · 2025: 15 · 2024: 14 · 2023: 6 · 2022: 7 · 2021: 12 · 2020: 12 · 2019: 13 · 2018: 12 · 2017: 15 · 2016: 14 · 2015: 15 · 2014: 17 · 2013: 15 · 2012: 17
FWCI
4.07
Type
journal article
Language
en
Open access
closed
Locations
American Zoologist (publishedVersion)
Topics
  • Social Sciences › Decision Sciences › General Decision Sciences › Decision-Making and Behavioral Economics
  • Life Sciences › Agricultural and Biological Sciences › Ecology, Evolution, Behavior and Systematics › Animal Behavior and Reproduction
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Neural and Behavioral Psychology Studies
Keywords
delay discounting, hyperbolic discounting, exponential discounting, delayed rewards, risk-sensitive foraging, waiting time, prey selection, patch selection, foraging decisions

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review