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In economics, hyperbolic discounting is a time-''inconsistent'' model of discounting. The discounted utility approach: Intertemporal choices are no different from other choices, except that some consequences are delayed and hence must be anticipated and discounted (i.e., reweighted to take into account the delay). 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. This process is traditionally modeled in form of exponential discounting, a time-''consistent'' model of discounting. A large number of studies have since demonstrated that the constant discount rate assumed in exponential discounting is systematically being violated. Hyperbolic discounting is a particular mathematical model devised as an improvement over exponential discounting, in the sense that it better fits the experimental data about actual behavior. But note, the time inconsistency of this behavior has some quite perverse consequences. Hyperbolic discounting has been observed in both human and non-human 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 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?" For certain range of offerings, 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. Individuals with such preferences are described as "present-biased". Individuals using hyperbolic discounting reveal a strong tendency to make choices that are inconsistent over time – they make choices today that their future self would prefer not to have made, despite using the same reasoning. This dynamic inconsistency happens because the value of future rewards is much lower under hyperbolic discounting than under exponential 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. That is, subjects' choices "match" these parameters. After the report of this effect in the case of delay, 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, and that when the larger, later reward is preferred, this preference can be reversed by reducing both rewards' delays by the same absolute amount. That is, for values of ''x'' for which under current conditions it would be obviously rational to prefer ''x'' dollars in (''n'' + 1) days over one dollar in ''n'' days (''e.g.'', ''x'' = 3), a large subset of the population would (rationally) prefer the former alternative given large values of ''n'', but even among this subset, a large (sub-)subset would (irrationally) prefer one dollar in ''n'' days when ''n'' = 0. Ainslie demonstrated the predicted reversal to occur among pigeons. 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. 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. Some evidence suggests pathological gamblers also discount delayed outcomes at higher rates than matched controls. 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 and cocaine than lower-rate discounters. Likewise, some have suggested that high-rate hyperbolic discounting makes unpredictable (gambling) outcomes more satisfying. 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.〔 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「hyperbolic discounting」の詳細全文を読む スポンサード リンク
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