The q-Exponential Social Discounting Functions of Gain and Loss

DOI: 10.4236/am.2013.43066   PDF   HTML   XML   6,699 Downloads   14,420 Views   Citations

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.

Share and Cite:

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.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[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

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.