Psychophysical Neuroeconomics of Decision Making: Nonlinear Time Perception Commonly Explains Anomalies in Temporal and Probability Discounting

ABSTRACT

Anomalies in decision over time (e.g., “hyperbolic time discounting”) and under risk (e.g., Allais paradox and hyperbolic probability discounting) have been attracting attention in behavioral and neuroeconomics. We have proposed that psychophysical time commonly explains anomalies in both decisions (Takahashi, 2011, Physica A; Takahashi*et* *al*., 2012, J Behav Econ & Finance). By adopting the *q*-exponential time and probability discounting models, our psychophysical and behavioral economic experiment confirmed that nonlinear distortion of psychophysical time is a common cause of the anomalies in decision both over time and under risk (*i*.*e*., intertemporal choice and decision under risk). Implications for psychophysical neuroeconomics and econophysics are discussed.

Anomalies in decision over time (e.g., “hyperbolic time discounting”) and under risk (e.g., Allais paradox and hyperbolic probability discounting) have been attracting attention in behavioral and neuroeconomics. We have proposed that psychophysical time commonly explains anomalies in both decisions (Takahashi, 2011, Physica A; Takahashi

Cite this paper

Takahashi, T. and Han, R. (2013) Psychophysical Neuroeconomics of Decision Making: Nonlinear Time Perception Commonly Explains Anomalies in Temporal and Probability Discounting.*Applied Mathematics*, **4**, 1520-1525. doi: 10.4236/am.2013.411205.

Takahashi, T. and Han, R. (2013) Psychophysical Neuroeconomics of Decision Making: Nonlinear Time Perception Commonly Explains Anomalies in Temporal and Probability Discounting.

References

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http://dx.doi.org/10.1186/1744-9081-3-52

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http://dx.doi.org/10.1143/JPSJ.81.104801

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http://dx.doi.org/10.1016/j.mehy.2005.04.040

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

http://dx.doi.org/10.1016/j.physa.2012.07.012

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http://dx.doi.org/10.2307/1914185

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http://dx.doi.org/10.2478/s11600-012-0005-0

[25] D. O. Cajueiro, “A Note on the Relevance of the q-Exponential Function in the Context of Intertemporal Choices,” Physica A: Statistical Mechanics and Its Applications, Vol. 364, 2006, pp. 385-388.

http://dx.doi.org/10.1016/j.physa.2005.08.056

[26] 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.

http://dx.doi.org/10.1016/j.physa.2007.11.047

[27] T. Takahashi, “Theoretical Frameworks for Neuro-Economics of Intertemporal Choice,” Journal of Neuroscience, Psychology, and Economics, Vol. 2, No. 2, 2009, pp. 75-90.

http://dx.doi.org/10.1037/a0015463

[28] T. Takahashi, “Molecular Neuroeconomics of Crime and Punishment: Implications for Neurolaw,” NeuroEndocrinology Letters, Vol. 33, No. 7, 2012, pp. 667-673.

[29] T. Takahashi, “A Probabilistic Choice Model Based on Tsallis’ Statistics,” Physica A: Statistical Mechanics and its Applications, Vol. 386, No. 1, 2007, pp. 335-338.

[30] T. Takahashi, R. Han, H. Nishinaka, T. Makino and H. Fukui, “The q-Exponential Probability Discounting of Gain and Loss,” Applied Mathematics, Vol. 4, No. 6, 2013, pp. 876-881.

http://dx.doi.org/10.4236/am.2013.46120

[31] 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. http://dx.doi.org/10.1016/j.physa.2007.03.038

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

http://dx.doi.org/10.1186/1744-9081-3-52

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

http://dx.doi.org/10.1186/1744-9081-3-20

[3] M. Asano, I. Basieva, A. Khrennikov, M. Ohya and I. Yamato, “Non-Kolmogorovian Approach to the ContextDependent Systems Breaking the Classical Probability Law,” Foundations of Physics, Vol. 43, No. 7, 2013, pp. 895-911. http://dx.doi.org/10.1007/s10701-013-9725-5

[4] J. R. Busemeyer, E. Pothos, R. Franco and J. S. Trueblood, “A Quantum Theoretical Explanation for Probability, Judgment ‘Errors’,” Psychological Review, Vol. 118, No. 2, 2011, pp. 193-218.

http://dx.doi.org/10.1037/a0022542

[5] T. Cheon and T. Takahashi, “Interference and Inequality in Quantum Decision Theory,” Physics Letters A, Vol. 375, No. 2, 2010, pp. 100-104.

http://dx.doi.org/10.1016/j.physleta.2010.10.063

[6] T. Cheon and T. Takahashi, “Quantum Phenomenology of Conjunction Fallacy,” Journal of the Physical Society of Japan, Vol. 81, No. 10, 2012, Article ID: 104801.

http://dx.doi.org/10.1143/JPSJ.81.104801

[7] T. Takahashi, “Quantum Decision Theory for Computational Psychiatry,” NeuroQuantology, Vol. 10, No. 4, 2012, pp. 688-691.

[8] A. Y. Khrennikov, “Ubiquitous Quantum Structure: From Psychology to Finance,” Springer-Verlag, Berlin, 2010.

http://dx.doi.org/10.1007/978-3-642-05101-2

[9] V. I. Yukalov and D. Sornette, “Decision Theory with Prospect Interference and Entanglement,” Theory and Decision, Vol. 70, No. 3, 2011, pp. 283-328.

http://dx.doi.org/10.1007/s11238-010-9202-y

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

[11] W. A. Wagenaar and S. Sagaria, “Misperception of Exponential Growth,” Perception and Psychophysics, Vol. 18, No. 6, 1975, pp. 416-422.

http://dx.doi.org/10.3758/BF03204114

[12] D. Prelec and G. Loewenstein, “Decision-Making over Time and under Uncertainty: A Common Approach,” Management Science, Vol. 37, No. 7, 1991, pp. 770-786.

http://dx.doi.org/10.1287/mnsc.37.7.770

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

[14] T. Takahashi, R. Han and F. Nakamura, “Time Discounting: Psychophysics of Intertemporal and Probabilistic Choices,” Journal of Behavioral Economics and Finance, Vol. 5, 2012, pp. 10-14.

[15] H. Rachlin, A. Raineri and D. Cross, “Subjective Probability and Delay,” Journal of Experimental Analysis of Behavior, Vol. 55, No. 2, 1991, pp. 233-244.

http://dx.doi.org/10.1901/jeab.1991.55-233

[16] P. A. Samuelson, “A Note on Measurement of Utility,” The Review of Economic Studies, Vol. 4, No. 2, 1937, pp. 155-161. http://dx.doi.org/10.2307/2967612

[17] R. H. Strotz, “Myopia and Inconsistency in Dynamic Utility Maximizatio,” Review of Economic Studies, Vol. 23, No. 3, 1955, pp. 165-180.

http://dx.doi.org/10.2307/2295722

[18] T. Takahashi, “Loss of Self-Control in Intertemporal Choice May Be Attributable to Logarithmic Time-Perception,” Medical Hypotheses, Vol. 65, No. 4, 2005, pp. 691-693.

http://dx.doi.org/10.1016/j.mehy.2005.04.040

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

http://dx.doi.org/10.1016/j.physa.2012.07.012

[20] T. Takahashi, “A Neuroeconomic Theory of Rational Addiction and Nonlinear Time-Perception,” Neuro Endocrinology Letters, Vol. 32, No. 3, 2011, pp. 221-225.

[21] J. von Neumann and O. Morgenstern, “Theory of Games and Economic Behavior,” Princeton University Press, Princeton, 1947.

[22] D. Kahneman and A. Tversky, “Prospect Theory: An Analysis of Decision under Risk,” Econometrica, Vol. 47, No. 2, 1979, pp. 263-292.

http://dx.doi.org/10.2307/1914185

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

[24] C. Tsallis, “Nonadditive Entropy Sq and Nonextensive Statistical Mechanics: Applications in Geophysics and Elsewhere,” ActaGeophysica, Vol. 60, No. 3, 2012, pp. 502-525.

http://dx.doi.org/10.2478/s11600-012-0005-0

[25] D. O. Cajueiro, “A Note on the Relevance of the q-Exponential Function in the Context of Intertemporal Choices,” Physica A: Statistical Mechanics and Its Applications, Vol. 364, 2006, pp. 385-388.

http://dx.doi.org/10.1016/j.physa.2005.08.056

[26] 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.

http://dx.doi.org/10.1016/j.physa.2007.11.047

[27] T. Takahashi, “Theoretical Frameworks for Neuro-Economics of Intertemporal Choice,” Journal of Neuroscience, Psychology, and Economics, Vol. 2, No. 2, 2009, pp. 75-90.

http://dx.doi.org/10.1037/a0015463

[28] T. Takahashi, “Molecular Neuroeconomics of Crime and Punishment: Implications for Neurolaw,” NeuroEndocrinology Letters, Vol. 33, No. 7, 2012, pp. 667-673.

[29] T. Takahashi, “A Probabilistic Choice Model Based on Tsallis’ Statistics,” Physica A: Statistical Mechanics and its Applications, Vol. 386, No. 1, 2007, pp. 335-338.

[30] T. Takahashi, R. Han, H. Nishinaka, T. Makino and H. Fukui, “The q-Exponential Probability Discounting of Gain and Loss,” Applied Mathematics, Vol. 4, No. 6, 2013, pp. 876-881.

http://dx.doi.org/10.4236/am.2013.46120

[31] 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. http://dx.doi.org/10.1016/j.physa.2007.03.038