while for q < 1, the discount rate is a decreasing function of delay D, resulting
in preference reversal over time. This can be seen by a direct calculation of the
time-derivative of the q-exponential discount rate:
k2(1 - q)
(d/dD) qEDR = - [kq(1 - q)D + 1]2 (3)
which is negative for q < 1, indicating ”decreasing impatience” for q smaller than
1. Also, impulsivity at delay D = 0 is equal to kq irrespective of q. Therefore, kq
and q can parameterize impulsivity and consistency, respectively, in a distinct
manner.
Regarding the neuropsychological processing underlying the q-exponential
discounting (i.e., inconsistent intertemporal choice), Takahashi (2005) proposed
that exponential discounting with logarithmic time-perception, τ(D) = α log(1+
βD), may explain dynamic inconsistency in intertemporal choice. If a subject
tries to discount a delayed reward exponentially with the logarithmic time-
perception (i.e., Weber-Fechner law in psychophysics), then F (τ) = exp(-kτ) =
1/(1 + βD)kα, which has the q-exponential functional form. Intuitively, subjects
try to discount exponentially (rationally and consistently), but actual intertem-
poral choice behavior may be hyperbolic and dynamically inconsistent, due to
a distortion in time-perception. This may also explain subadditive discount-
ing, because τ (D) is concave in delay D (i.e., the sub jective delay length is
larger when the delay is divided into shorter time-intervals than when the delay
is perceived as a single time-interval; for details see Takahashi, 2006). There-
fore, it can be expected that the non-linear psychophysical effects of temporal
cognition on intertemporal choice may be reflected in the q parameter in the
q-exponential discount function. However, to our knowledge, no study has yet
examined how psychological factors, such as attention to a time-interval between
sooner and later rewards, modulate intertemporal choice behavior by utilizing
the q-exponential function, although recent studies reported attention effects on
time modulated dynamic consistency in temporal discounting (Ebert & Prelec,
2007; Zauberman et al., 2008).
In the present study, we address the question of how cultural differences
in attention allocation (i.e., ”analytic” versus ”holistic” allocation) modulate
intertemporal choice behavior between American and Japanese decision makers.
3 Cultural neuroscience of attention and thought
In recent years, cultural psychologists have begun to show that there are sys-
tematic cultural variations in human (neuro)psychological processes (Markus &
Kitayama, 1991). These researchers assume that neuropsychological processes
are by nature socially driven. According to their theories, the neuropsycho-
logical processes are shaped through their interaction with cultural, social and
environmental factors. Based on this assumption, it has often been examined
how particular cognitive processes (e.g., attention allocation) could be mani-
fested in particular cultural contexts and how different cultural environments
in turn lead to the development of different patterns of ability. These studies
reported that East Asians’ patterns of attention were in general ”context depen-
dent”, whereas Westerners’ patterns of attention were ”context independent”.