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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 hyperbolic discounting curve is to askcompare short term preferences with long term preferences. For instance: "Would you prefer Aa dollar today or Bthree dollars tomorrow?" and then,or "Would you prefer Aa dollar in one year, or Bthree dollars 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>

For example in studies of pigeons, 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 either ask: "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?"  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>

Subjects using hyperbolic discounting reveal a strong tendency to make choices that are inconsistent over time.  In other words, they make choices today that their future self would prefer not to make, despite using the same reasoning.  This dynamic inconsistency <ref>Laibson, David, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, MIT Press, vol. 112(2), pages 443-77, May.
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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]]