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Given two similar rewards, humans show a preference for one that arrives sooner rather than later. Humans are said to ''discount'' the value of the later reward, by a factor that increases with the length of the delay.  In [[behavioral economics]], '''hyperbolic discounting''' is a particular mathematical model thought to approximate this discounting process; that is, it models how humans actually make such valuations.  Hyperbolic discounting is sharply different in form from [[exponential discounting]], a [[rationality|rational]] function used in [[finance]] used in the analysis of [[intertemporal choice|choice over time]].  Hyperbolic discounting has been observed in humans and animals.

In hyperbolic discounting, valuations fall very rapidly for small delay periods, but then fall slowly for longer delay periods.  This contrasts with exponential discounting, in which valuation falls by a constant factor per unit delay, regardless of the total length of the delay.  The standard experiment used to reveal a test subject's discounting curve is to ask: "Would you prefer A today or B tomorrow?" and then, "Would you prefer A in one year, or B in one year and one day?"

For example in studies of pigeons <ref>[[George Ainslie (psychologist)|Ainslie, G. W]]. (1974)  Impulse control in pigeons.  ''Journal of the Experimental Analysis of Behavior'' 21,485-489.</ref>, the pigeon is given two buttons: button A provides a small amount of food quickly while button B provides more seed but after a delay.   The bird then experiments for a while and settles on preferring A or B.<ref>[[George Ainslie (psychologist)|Ainslie, G. W]]. (1974)  Impulse control in pigeons.  ''Journal of the Experimental Analysis of Behavior'' 21,485-489.</ref>  With humans the typical experiment might ask: 'Would you prefer a dollar today or three dollars (today vs. tomorrow) or (in one year vs. in one year and one day)?"  Typically, subjects will take less money today versus tomorrow, but will gladly wait one extra day in a year in order to receive more money.<ref>Thaler, R. H. (1981) Some Empirical Evidence on Dynamic Inconsistency. ''Economic Letters'' 8, 201-07.</ref>

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which is exactly the hyperbolic discount rate. Similar conclusions can be obtained from other plausible distributions for <math>\lambda</math>. <ref name="sozou1998"/>

==Applications==

More recently these observations about [[discount function]]s have been used to study saving for retirement, borrowing on credit cards, and [[procrastination]]. However, hyperbolic discounting has been most frequently used to explain [[
Substance dependence|addiction]].

==See also==
* [[Time value of money]]
* [[Time preference]]
* [[Intertemporal choice]]
* [[deferred gratification]]

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* Rachlin, H. (2000). ''The Science of Self-Control'' Cambridge;London: Harvard University Press
* Raineri,A., and Rachlin, H. (1993). The effect of temporal constraints on the value of money and other commodities. ''Journal of Behavioral Decision-Making, 6,'' 77-94.

[[Category:Cognitive biases]]
[[Category:Behavioral finance]]

[[pl:Hiperboliczne obniżenie wartości]]