Discounting future reward in an uncertain world: behavioural data

Humans discount delayed relative to more immediate reward. A plausible
explanation is that impatience arises partly from uncertainty, or risk,
implicit in delayed reward. Existing theories of discounting-as-risk focus
on a probability that delayed reward will not materialize. By contrast, we
examine how uncertainty in the magnitude of delayed reward contributes to
delay discounting. We propose a model wherein reward is discounted
proportional to the rate of random change in its magnitude across time,
termed volatility. We find evidence to support this model across three
experiments (total N=158). Firstly, using a task where participants chose
when to sell products, whose price dynamics they previously learned, we
show discounting increases in line with price volatility. Secondly, we
show that this effect pertains over naturalistic delays of up to four
months. Using functional magnetic resonance imaging, we observe a
volatility-dependent decrease in functional hippocampal-prefrontal
coupling during intertemporal choice. Thirdly, we replicate these effects
in a larger online sample, finding that volatility discounting within each
task correlates with baseline discounting outside of the task. We conclude
that delay discounting partly reflects time-dependent uncertainty about
reward magnitude, i.e. volatility. Our model captures how discounting
adapts to volatility, thereby partly accounting for individual differences
in impatience. Our imaging findings suggest a putative mechanism whereby
uncertainty reduces prospective simulation of future outcomes.