A Neuroeconomic Theory of Rational Addiction and Nonlinear Time-Perception

Abstract

Neuroeconomic conditions for "rational addiction" (Becker and Murphy, 1988) have been unknown. This paper derived the conditions for "rational addiction" by utilizing a nonlinear time-perception theory of "hyperbolic" discounting, which is mathematically equivalent to the q-exponential intertemporal choice model based on Tsallis' statistics. It is shown that (i) Arrow-Pratt measure for temporal cognition corresponds to the degree of irrationality (i.e., Prelec's "decreasing impatience" parameter of temporal discounting) and (ii) rationality in addicts is controlled by a nondimensionalization parameter of the logarithmic time-perception function. Furthermore, the present theory illustrates the possibility that addictive drugs increase impulsivity via dopaminergic neuroadaptation without increasing irrationality. Future directions in the application of the model to studies in neuroeconomics are discussed.

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

“…The common time-perception account of anomalies in decision over time and under risk in psychophysical neuroeconomics [2,3,7,9,16] has, for the first time, been confirmed in the present experimental study. Our current study has adopted the perspective of psychophysical law of time perception to account for those anomalies.…”

“…Therefore, introducing logarithmic psychophysical time (Equation (4)) into the time discount function (Equation (2)) can express a hyperbola-like function (Equation (5)). [8] empirically demonstrated that when logarithmic psychophysical time was introduced into the time discounting model, the functional form of time discount model was closer to exponential than hyperbolic, supporting Takahashi's logarithmic time perception theory of non-exponential discounting [7,9].…”

Quantum Decision Theory for Computational Psychiatry

“…For instance, Takahashi et al, (2008) demonstrated the irrationality observed in decision over time by depressed patients with a neuroeconomic model of intertemporal choice. Takahashi (2011) also proposed a neuroeconomic framework for the assessment of rationality in intertemporal decision-making in addicts, by incorporating nonlinear temporal cognition theory of intertemporal choice (Takahashi, 2005). On the other hand, in mathematical cognitive science, mathematical frameworks of "quantum decision theory" have been proposed to explain human probability judgment errors (Busemeyer et al, 2011;Cheon and Takahashi, 2010;Franco, 2009;Khrennikov, 2010).…”

Meaning and Development of Generalizing Extensive Structures

“…(14), Before closing the section, we shall discuss the possibility of applying the theory of the generalized extensive structure with right action to problems in the field of psychology and psychotherapy. The relationship [9][10][11][12] between psychiatric problems (e.g. depression, addiction, obesity and suicide) and temporal discounting has already been investigated.…”

“…More precisely, by using a particular discount function (which can be transformed to the generalized hyperbolic discount function), it was reported by Takahashi et al [9] that depressive patients were more impatient and inconsistent in temporal choice (which means timedependency of impatience) than healthy control subjects. Additionally, Takahashi [10][11][12] emphasized the significance of observing the variation of two parameters in the discount function regarding both impatience and inconsistency for patients with the above-mentioned psychiatric diseases, because neurobiological substrates (e.g. serotonin, dopamine and steroid hormones) are not only related to the above diseases but also somewhat correlated with temporal discounting and time perception.…”