The *q*-Exponential Social Discounting Functions of Gain and Loss

ABSTRACT

Social discounting has been attracting attention in behavioral psychology, econophysics, and neuroeconomics. Several mathematical models have been proposed for social discounting; exponential discounting, hyperbolic discounting, a *q-*exponential discounting model based on Tsallis’ statistics. In order to experimentally examine the mathematical characteristics of the* q-*exponential social discounting models for gain and loss in humans, we estimated the parameters of the *q-*exponential social discounting models by assessing the points of subjective equality (indifference points) at seven social distances. We observed that gain was more steeply social-discounted than loss. Usefulness of the *q-*exponential social discounting model in social physics, econophysics, and cultural neuroeconomics are discussed.

KEYWORDS

Social Discounting; Altruism; Neuroeconomics; Econophysics; Sociophysics; Tsallis’ Statistics

Social Discounting; Altruism; Neuroeconomics; Econophysics; Sociophysics; Tsallis’ Statistics

Cite this paper

T. Takahashi, "The*q*-Exponential Social Discounting Functions of Gain and Loss," *Applied Mathematics*, Vol. 4 No. 3, 2013, pp. 445-448. doi: 10.4236/am.2013.43066.

T. Takahashi, "The

References

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[4] T. Takahashi, H. Oono and M. H. B. Radford, “Empirical Estimation of Consistency Parameter in Intertemporal Choice Based on Tsallis’ Statistics,” Physica A: Statistical Mechanics and Its Applications, Vol. 381, 2007, pp. 338-342.

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[19] W. Du, L. Green and J. Myerson, “Cross-Cultural Comparisons of Discounting Delayed and Probabilistic Rewards,” Psychological Record, Vol. 52, No. 4, 2002, pp. 479-492.

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[1] C. Tsallis, “Nonadditive Entropy Sq and Nonextensive Statistical Mechanics: Applications in Geophysics and Elsewhere,” Acta Geophysica, Vol. 60, No. 3, 2012, pp. 502-525. doi:10.2478/s11600-012-0005-0

[2] C. Tsallis, C. Anteneodo, L. Borland and R. Osorio, “Non-Extensive Statistical Mechanics and Economics,” Physica A: Statistical Mechanics and Its Applications, Vol. 324, No. 1, 2003, pp. 89-100.

[3] T. Takahashi, “A Comparison of Intertemporal Choices for Oneself versus Someone Else Based on Tsallis’ Statistics,” Physica A: Statistical Mechanics and Its Applications, Vol. 385, No. 2, 2007, pp. 637-644.

[4] T. Takahashi, H. Oono and M. H. B. Radford, “Empirical Estimation of Consistency Parameter in Intertemporal Choice Based on Tsallis’ Statistics,” Physica A: Statistical Mechanics and Its Applications, Vol. 381, 2007, pp. 338-342.

[5] T. Takahashi, H. Oono and M. H. B. Radford, “Comparison of Probabilistic Choice Models in Humans,” Behavioral and Brain Functions, Vol. 3, No. 1, 2007, p. 20.

[6] T. Takahashi, K. Ikeda and T. Hasegawa, “A Hyperbolic Decay of Subjective Probability of Obtaining Delayed Rewards,” Behavioral and Brain Functions, Vol. 3, 2007, p. 52.

[7] T. Takahashi, “A Comparison between Tsallis’s Statistics-Based and Generalized Quasi-Hyperbolic Discount Models in Humans,” Physica A: Statistical Mechanics and Its Applications, Vol. 387, 2008, pp. 551-566.

[8] T. Takahashi, “Tsallis’s Non-Extensive Free Energy as a Subjective Value of an Uncertain Reward,” Physica A: Statistical Mechanics and Its Applications, Vol. 388, No. 5, 2009, pp.715-719.

[9] T. Takahashi, “Theoretical Frameworks for Neuroeconomics of Intertemporal Choice,” Journal of Neuroscience, Psychology, and Economics, Vol. 2, No. 2, 2009, pp. 75-90. doi:10.1037/a0015463

[10] T. Takahashi, T. Hadzibeganovic, S. A. Cannas, T. Makino, H. Fukui and S. Kitayama, “Cultural Neuroeconomics of Intertemporal Choice,” Neuro Endocrinology Letters, Vol. 30, No. 2, 2009, pp. 185-191.

[11] T. Takahashi, “A Social Discounting Model Based on Tsallis’ Statistics,” Physica A: Statistical Mechanics and Its Applications, Vol. 389, No. 17, 2010, pp. 3600-3603.

[12] T. Takahashi, “Psychophysics of the Probability Weighting Function,” Physica A: Statistical Mechanics and Its Applications, Vol. 390, No. 5, 2011, pp. 902-905.

[13] R. Han and T. Takahashi, “Psychophysics of Time Perception and Valuation in Temporal Discounting of Gain and Loss,” Physica A: Statistical Mechanics and Its Applications, Vol. 391, No. 24, 2012, pp. 6568-6576.

[14] T. Takahashi, H. Oono and M. H. B. Radford, “Psychophysics of Time Perception and Intertemporal Choice Models,” Physica A: Statistical Mechanics and Its Applications, Vol. 387, No. 8-9, 2008, pp. 2066-2074.

[15] B. Jones and H. Rachlin, “Social Discounting,” Psychological Science, Vol. 17, No. 4, 2006, pp. 283-286. doi:10.1111/j.1467-9280.2006.01699.x

[16] H. Rachlin and B. Jones, “Social Discounting and Delay Discounting,” Journal of Behavioral Decision Making, Vol. 21, No. 1, 2008, pp. 29-43. doi:10.1002/bdm.567

[17] U. Benzion, A. Rapoport and J. Yagil, “Discount Rates Inferred from Decisions: An Experimental Study,” Management Science, Vol. 35, No. 3, 1989, pp. 270-284. doi:10.1287/mnsc.35.3.270

[18] Y. Ohmura, T. Takahashi and N. Kitamura, “Discounting Delayed and Probabilistic Monetary Gains and Losses by Smokers of Cigarettes,” Psychopharmacology, Vol. 182, No. 4, 2005, pp. 508-515. doi:10.1007/s00213-005-0110-8

[19] W. Du, L. Green and J. Myerson, “Cross-Cultural Comparisons of Discounting Delayed and Probabilistic Rewards,” Psychological Record, Vol. 52, No. 4, 2002, pp. 479-492.

[20] S. J. Estle, L. Green, J. Myerson and D. D Holt, “Differential Effects of Amount on Temporal and Probability Discounting of Gains and Losses,” Memory & Cognition, Vol. 34, No. 4, 2006, pp. 914-928. doi:10.3758/BF03193437