The *q*-Exponential Probability Discounting of Gain and Loss ()

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.

**DOI: **10.4236/am.2013.46120
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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.

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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. doi: 10.4236/am.2013.46120.

Conflicts of Interest

The authors declare no conflicts of interest.

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