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A generalization of the \(q\)-exponential discounting function. (English) Zbl 1402.91131
Summary: The aim of this paper is to generalize the \(q\)-exponential discounting function introduced by D. O. Cajueiro [“A note on the relevance of the q-exponential function in the context of intertemporal choices”, Physica A 364, 385–388 (2006; doi:10.1016/j.physa.2005.08.056)] using the hyperbolic function as a base. The presented generalization has two aspects. First, we consider any discounting function \(F(t)\), and not just hyperbolic discounting. Second, the value of the parameter \(q\) is extended to the joint interval \((- \infty, 1) \cup(1, + \infty)\). In this way, we have found a family of discounting functions whose elements are subadditive or superadditive according to the value of \(q\).

MSC:
91B16 Utility theory
91B06 Decision theory
91B80 Applications of statistical and quantum mechanics to economics (econophysics)
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[1] Cajueiro, D. O., A note on the relevance of the q-exponential function in the context of intertemporal choices, Physica A, 364, 385-388, (2006)
[2] Tsallis, C., What are the numbers that experiments provide?, Química Nova, 17, 6, 468-471, (1994)
[3] Takahashi, T., A comparison of intertemporal choices for oneself versus someone else based on tsallis’ statistics, Physica A, 385, 637-644, (2007)
[4] Takahashi, T., A comparison between tsallis’s statistics-based and generalized quasi-hyperbolic discount models in humans, Physica A, 387, 551-556, (2008)
[5] Han, R.; Takahashi, T., Psychophysics of time perception and valuation in temporal discounting of gain and loss, Physica A, 391, 6568-6576, (2012)
[6] Cruz-Rambaud, S.; Muñoz-Torrecillas, M. J., An analysis of the anomalies in traditional discounting models, International Journal of Psychology and Psychological Therapy, 4, 1, 105-128, (2004)
[7] Scholten, M.; Read, D., Discounting by intervals: a generalized model of intertemporal choice, Management Science, 52, 1424-1436, (2006)
[8] Green, L.; Myerson, J., Exponential versus hyperbolic discounting of delayed outcomes: risk and waiting time, American Zoologist, 36, 496-505, (1996)
[9] Read, D., Is time-discounting hyperbolic or subadditive?, Journal of Risk and Uncertainty, 23, 1, 5-32, (2001) · Zbl 0986.91013
[10] Read, D., Subadditive intertemporal choice, (Loewenstein, G.; Read, D.; Baumeister, R., Time and Decision: Economic and Psychological Perspectives on Intertemporal Choice, (2003), Russell Sage Foundation New York), 301-322
[11] Cruz-Rambaud, S.; Muñoz-Torrecillas, M. J., Intransitive preference relations and subadditivity, (D’Ambra, L.; Rostirolla, P.; Squillante, M., Metodi, modelli e tecnologie dell’informazione a supporto delle decisioni. I. Metodologie, (2008), FrancoAngeli Milano), 137-142
[12] Cruz-Rambaud, S.; Muñoz-Torrecillas, M. J., Delay and interval effects with subadditive discounting functions, (Greco, S.; Marques Pereira, R. A.; Squillante, M.; Yager, R. R.; Kacprzyk, J., Preferences and Decisions. Models and Applications (Studies in fuzziness and soft computing), (2010), Springer-Verlag Berlin Heidelberg), 85-110 · Zbl 1202.91089
[13] Cruz-Rambaud, S.; Ventre, A. G.S., Decomposable financial laws and profitability, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 6, 4, 329-344, (1998) · Zbl 1087.91512
[14] Harvey, C., Value functions for infinite-period planning, Management Science XXXII, 1123-1139, (1986) · Zbl 0602.90036
[15] McAlvanah, P., Subadditivity, patience, and utility: the effects of dividing time intervals, Journal of Economic Behavior & Organization, 76, 2, 325-337, (2010)
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