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.