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Applied Mathematics 2013年第11期4卷 1520-1525页

作者： Taiki Takahashi Ruokang Han Center for Experimental Research in Social Science Department of Behavioral Science Faculty of Letters Hokkaido University Sapporo Japan

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.

关键词： Psychophysics Discounting Neuroeconomics Econophysics tsallis’ Statistics

The q-Exponential Probability Discounting of Gain and Loss

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Applied Mathematics 2013年第6期4卷 876-881页

作者： Taiki Takahashi Ruokang Han Hiroshi Nishinaka Takaki Makino Hiroki Fukui Department of Behavioral Science Center for Experimental Research in Social Science Faculty of Letters Hokkaido University Sapporo Japan Department of Forensic Psychiatry National Institute of Mental Health National Center of Neurology and Psychiatry Tokyo Japan

Probability discounting is defined as the devaluation of outcomes as the probability of receiving or paying those decreases. A q-exponential probability discounting model based on tsallis’ statistics has been proposed in econophysics (Takahashi, 2007, Physica A). We examined (a) fitness of the models to behavioral data of probability discounting of both gain and loss;and (b) relationships between parameters in the q-exponential probability discounting model across gain and loss. Our results demonstrated that, for both gain and loss, the q-exponential model better fits the behavioral data than exponential and hyperbolic functions, and there is the sign effect in q-exponential probability discounting. Relationships between Kahneman-Tversky’s prospect theory in behavioral economics and the q-exponential probability discounting are high-lightened.

关键词： Probability Discounting Neuroeconomics Econophysics tsallis’ Statistics

The q-Exponential Social Discounting Functions of Gain and Loss

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Applied Mathematics 2013年第3期4卷 445-448页

作者： Taiki Takahashi Hokkaido University Sapporo Japan

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.

关键词： Social Discounting Altruism Neuroeconomics Econophysics Sociophysics tsallis’ Statistics

Mathematical Neurolaw of Crime and Punishment: The q-Exponential Punishment Function

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Applied Mathematics 2013年第10期4卷 1371-1375页

作者： Taku Yokoyama Taiki Takahashi Department of Behavioral Science Center for Experimental Research in Social Science Faculty of Letters Hokkaido University Sapporo Japan

Whether people tend to punish criminals in a socially-optimal manner (i.e., hyperbolic punishment) or not is unknown. By adopting mathematical models of probabilistic punishment behavior (i.e., exponential, hyperbolic, and q-exponential probability discounting model based on tsallis thermodynamics and neuroeconomics, Takahashi, 2007, Physica A;Takahashi et al., 2012, Applied Mathematics), we examined 1) fitness of the models to behavioral data of uncertain punishment, and 2) deviation from the socially optimal hyperbolic punishment function. Our results demonstrated that, the q-exponential punishment function best fits the behavioral data, and people overweigh the severity of punishment at small punishing probabilities and underweigh the severity of punishment at large punishing probabilities. In other words, people tend to punish crimes too severely and mildly with high and low arrest rate (e.g., homicide vs. excess of speed limit), respectively. Implications for neuroeconomics and neurolaw of crime and punishment (Takahashi, 2012, NeuroEndocrinology Letters) are discussed.

关键词： Neurolaw Neuroeconomics Econophysics tsallis’ Statistics Hyperbolic Punishment Function

An Experimental Comparison of Quantum Decision Theoretical Models of Intertemporal Choice for Gain and Loss

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Journal of Quantum Information Science 2012年第4期2卷 119-122页

作者： Taiki Takahashi Hiroshi Nishinaka Takaki Makino Ruokang Han Hiroki Fukui Department of Behavioral Science Center for Experimental Research in Social Science Hokkaido University Sapporo Japan Department of Forensic Psychiatry National Institute of Mental Health National Center of Neurology and Psychiatry Tokyo Japan

In mathematical physics and psychology, “quantum decision theory” has been proposed to explain anomalies in human decision-making. One of such quantum models has been proposed to explain time inconsistency in human decision over time. In this study, we conducted a behavioral experiment to examine which quantum decision models best account for human intertemporal choice. We observed that a q-exponential model developed in tsallis’ thermodynamics (based on Takahashi’s (2005) nonlinear time perception theory) best fit human behavioral data for both gain and loss, among other quantum decision models.

关键词： Discounting Neuroeconomics Econophysics Quantum Decision Theory tsallis’ Statistics