What is Hyperbolic Discounting How Does Hyperbolic Discounting Apply to Marketing

What is Hyperbolic Discounting? How Does Hyperbolic Discounting Apply to Marketing?

Definition:

Hyperbolic discounting happens when people show a preference for a reward that arrives sooner rather than later.

According to hyperbolic discounting, valuations fall relatively rapidly for earlier delay periods (as in, from now to one week), but then fall more slowly for longer delay periods (for instance, more than a few days).

For example, in an early study subjects said they would be indifferent between receiving $15 immediately or $30 after 3 months, $60 after 1 year, or $100 after 3 years. These indifferences reflect annual discount rates that declined from 277% to 139% to 63% as delays got longer.[5] This contrasts with exponential discounting, in which valuation falls by a constant factor per unit delay and the discount rate stays the same.

The standard experiment used to reveal a test subject’s hyperbolic discounting curve is to compare short-term preferences with long-term preferences. For instance: “Would you prefer a dollar today or three dollars tomorrow?” or “Would you prefer a dollar in one year or three dollars in one year and one day?”

It has been claimed that a significant fraction of subjects will take the lesser amount today, but will gladly wait one extra day in a year in order to receive the higher amount instead.[5]

Hyperbolic Discounting Observations:

The phenomenon of hyperbolic discounting is implicit in Richard Herrnstein’s “matching law“, which states that when dividing their time or effort between two non-exclusive, ongoing sources of reward, most subjects allocate in direct proportion to the rate and size of rewards from the two sources, and in inverse proportion to their delays.[7] That is, subjects’ choices “match” these parameters.

After the report of this effect in the case of delay,[8] George Ainslie pointed out that in a single choice between a larger, later and a smaller, sooner reward, inverse proportionality to delay would be described by a plot of value by delay that had a hyperbolic shape. When the smaller, sooner reward is preferred, this preference can be reversed by increasing both rewards’ delays by the same absolute amount.

Ainslie’s research showed that a substantial number of subjects reported that they would prefer $50 immediately rather than $100 in six months, but would NOT prefer $50 in 3 months rather than $100 in nine months, even though this was the same choice seen at 3 months’ greater distance.

More significantly, those subjects who said they preferred $50 in 3 months to $100 in 9 months said they would NOT prefer $50 in 12 months to $100 in 18 months—again, the same pair of options at a different distance—showing that the preference-reversal effect did not depend on the excitement of getting an immediate reward.[9] Nor does it depend on human culture; the first preference reversal findings were in rats and pigeons.[10][11][12]

A large number of subsequent experiments have confirmed that spontaneous preferences by both human and nonhuman subjects follow a hyperbolic curve rather than the conventional, exponential curve that would produce consistent choice over time.[13][14]

For instance, when offered the choice between $50 now and $100 a year from now, many people will choose the immediate $50. However, given the choice between $50 in five years or $100 in six years almost everyone will choose $100 in six years, even though that is the same choice seen at five years’ greater distance.

Hyperbolic discounting has also been found to relate to real-world examples of self-control. Indeed, a variety of studies have used measures of hyperbolic discounting to find that drug-dependent individuals discount delayed consequences more than matched nondependent controls, suggesting that extreme delay discounting is a fundamental behavioral process in drug dependence.[15][16][17]

Some evidence suggests pathological gamblers also discount delayed outcomes at higher rates than matched controls.[18]

Whether high rates of hyperbolic discounting precede addictions or vice versa is currently unknown, although some studies have reported that high-rate discounters are more likely to consume alcohol[19] and cocaine[20] than lower-rate discounters. Likewise, some have suggested that high-rate hyperbolic discounting makes unpredictable (gambling) outcomes more satisfying.[21]

The degree of discounting is vitally important in describing hyperbolic discounting, especially in the discounting of specific rewards such as money. The discounting of monetary rewards varies across age groups due to the varying discount rate.[13] The rate depends on a variety of factors, including the species being observed, age, experience, and the amount of time needed to consume the reward.[22][23]

See Also: Time value of money, Time preference, Intertemporal choice, Deferred gratification, Akrasia, Temporal motivation theory

References

  1. Poling, A., Edwards, T. L., Weeden, M., & Foster, T. (2011). The matching law. Psychological Record, 61(2), 313-322.
  2. Simon, C., & Baum, W. M. (2017). Allocation of Speech in Conversation. Journal of Experimental Analysis of Behavior, 107.
  3. Herrnstein, R.J. (1961). Relative and absolute strength of responses as a function of frequency of reinforcement. Journal of the Experimental Analysis of Behaviour, 4, 267–72.
  4. Baum, W.M. (1974). On two types of deviation from the matching law: Bias and undermatching. Journal of the Experimental Analysis of Behavior, 22, 231–42.
  5. Davison, M. & McCarthy, D. (1988). The matching law: A research review. Hillsdale, NJ: Erlbaum.
  6. Herrnstein, R.J. (1970). On the law of effect. Journal of the Experimental Analysis of Behavior, 13, 243–66.
  7. Skinner, B. F. (1971)Beyond Freedom and Dignity, New Yori:Knopf
  8. Bradshaw, C.M.; Szabadi, E. & Bevan, P. (1976). Behavior of humans in variable-interval schedules of reinforcement Journal of the Experimental Analysis of Behavior, 26, 135–41.
  9. Horne, P.J. & Lowe, C.F. (1993). Determinants of human performance on concurrent schedules. Journal of the Experimental Analysis of Behavior, 59, 29–60. doi:10.1901/jeab.1993.59-29
  10. Strand, P.S. (2001) Momentum, Matching, and Meaning: Toward a Fuller Exploitation of Operant Principles. The Behavior Analyst Today, 2(3), 170–84
  11. James Snyder, Mike Stoolmiller, Gerald R. Patterson, Lynn Schrepferman, Jessica Oeser, Kassy Johnson, and Dana Soetaert (2003): The Application of Response Allocation Matching to Understanding Risk Mechanisms in Development: The Case of Young Children’s Deviant Talk and Play, and Risk for Early-Onset Antisocial Behavior. The Behavior Analyst Today, 4(4), 435–45 “Archived copy” (PDF). Archived from the original (PDF) on 2011-08-24. Retrieved 2011-11-17.
  12. Snyder, J.J. & Patterson, G.R. (1995). Individualized differences in social aggression: A test of the reinforcement hypothesis in the natural environment. Behavior Therapy, 26, 371–91.
  13. Baum, W.M. (1974). On two types of deviation from the matching law: Bias and undermatching. Journal of the Experimental Analysis of Behavior, 22, 231–42.
  14. Bradshaw, C.M.; Szabadi, E. & Bevan, P. (1976). Behavior of humans in variable-interval schedules of reinforcement Journal of the Experimental Analysis of Behavior, 26, 135–41.
  15. Davison, M. & McCarthy, D. (1988). The matching law: A research review. Hillsdale, NJ: Erlbaum.
  16. Herrnstein, R.J. (1961). Relative and absolute strength of responses as a function of frequency of reinforcement. Journal of the Experimental Analysis of Behaviour, 4, 267–72.
  17. Herrnstein, R.J. (1970). On the law of effect. Journal of the Experimental Analysis of Behavior, 13, 243–66.
  18. Horne, P.J. & Lowe, C.F. (1993). Determinants of human performance on concurrent schedules. Journal of the Experimental Analysis of Behavior, 59, 29–60. doi:10.1901/jeab.1993.59-29.
  19. Poling, A., Edwards, T. L., Weeden, M., & Foster, T. (2011). The matching law. Psychological Record, 61(2), 313-322.
  20. Simon, C., & Baum, W. M. (2017). Allocation of Speech in Conversation. Journal of Experimental Analysis of Behavior, 107.
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