انرژی رایگان غیر گسترده Tsallis 'به عنوان یک ارزش ذهنی از پاداش نامشخص

Recent studies in neuroeconomics and econophysics revealed the importance of reward expectation in decision under uncertainty. Behavioral neuroeconomic studies have proposed that the unpredictability and the probability of an uncertain reward are distinctly encoded as entropy and a distorted probability weight, respectively, in the separate neural systems. However, previous behavioral economic and decision-theoretic models could not quantify reward-seeking and uncertainty aversion in a theoretically consistent manner. In this paper, we have: (i) proposed that generalized Helmholtz free energy in Tsallis’ non-extensive thermostatistics can be utilized to quantify a perceived value of an uncertain reward, and (ii) empirically examined the explanatory powers of the models. Future study directions in neuroeconomics and econophysics by utilizing the Tsallis’ free energy model are discussed.

Humans and non-human animals devalue probabilistic rewards as the receipt becomes more uncertain. The preference for a certain reward over an uncertain reward of an equal expected value is referred to as risk aversion in decision-making under risk/uncertainty. Neuropsychopharmacological studies reported that several types of neurochemical substances such as nicotine and serotonin dramatically modulate human decision under uncertainty [1] and [2]. In microeconomic theory, risk aversion is represented by a concave utility function [3]. Decision-making under uncertainty has been drawing much attention in behavioral neuroeconomics, econophysics and neurofinance, because departures from the prediction of the microeconomic theory (i.e., anomalies) have repeatedly been demonstrated in human choice behavior [4], [5], [6] and [7]. To establish quantitatively precise models of actual human decision-making under risk is important for understanding financial markets, risky decision by substance abusers and pathological gamblers [1] and [8]. Notably, neuroimaging studies have identified neural activities associated with uncertainty in decision under risk [9], [8] and [10]. Empirical studies in behavioral neuroeconomics on decision-making under risk and uncertainty have reported the following important findings: (A) People overweight small probabilities and underweight large probabilities [11]; (B) People have aversion to “ignorance” on the outcomes of uncertain rewards (i.e., people prefer a predictable outcome to an unpredictable one) [4]. It is important to note that von Neumann–Morgenstern’s traditional expected utility theory [3] cannot predict/explain these psychological tendencies observed in humans. In order to explain and formalize anomaly (A), the prospect theory (PT) has been proposed [11]. In PT, it is assumed that a probability of an uncertain reward is nonlinearly transformed/distorted into a psychophysical “probability weight” function [5] and [6] which is concave in probability at small probabilities and convex at large probabilities. Anomaly (B) has most dramatically been demonstrated in the Ellsberg paradox experiment in which people prefer uncertain rewards with a known probability distribution to an unknown probability distribution [4]. In order to quantify human aversion to ignorance on outcomes with known probabilities, Shannon entropy has been introduced [12]. However, to date, little effort has been spent on unifying PT and Tsallis thermostatistics-based decision theory, and combining the psychophysical and information-theoretic factors in decision under risk. It is to be noted that Antenedo, Tsallis & Martinez (2002) [13] is a pioneering investigation into this direction. Cajueiro (2006)’s attempt [14] to apply Tsallis’ statistics-based deformed algebra to intertemporal choice and empirical estimation of parameters in the model [15] are also in a similar line to the present study. This paper is organized in the following manner. In Section 2, I briefly introduce PT and the role of entropy in decision under risk, in Section 3, I explain that a generalized free energy in Tsallis’ non-extensive thermostatistics can be utilized as a subjective value of an uncertain reward, and in Section 4, an experimental comparison between the previously-proposed entropy model and the present Tsallis’ generalized free energy models is reported. Finally, in Section 5, I suggest some conclusions from this study and future study directions by utilizing the present Tsallis’ free energy model.

The present study shows that the coefficient of Tsallis’ generalized entropy may be able to parameterize subject’s unpredictability aversion. It is to be noted that in decision under uncertainty with an unknown probability distribution (“ambiguity” or Knightian uncertainty), subjective probability is known to be non-additive [4] and [21]. Therefore, human decision under ambiguity may also be described with a non-extensive model based on Tsallis’ thermostatistics. Also, future studies in neuroeconomics should examine the relations between subjects’ TqTq parameter values and neural activities encoding unpredictability aversion [10]. Regarding neurofinance and econophysics, the present model may be useful because we have shown that aggregated human probabilistic choice may be described with entropy-based models better than other well-known models such as Prelec’s probability weight function [5] (often adopted in behavioral economics) and the one-parameter hyperbolic probability discount function (often adopted in psychopharmacology) [22].