Hugo Mell, Nicolas Baumard, Jean-Baptiste André

Individuals exposed to deprivation tend to show a characteristic behavioural syndrome suggestive of a short time horizon. This pattern has traditionally been attributed to the intrinsically higher unpredictability of deprived environments, which renders waiting for long term rewards more risky (i.e. collection risks are high). In the current paper, based on a simple dynamic life history model, we show that a significant portion of individuals’ propensity to discount future rewards might have a completely distinct origin. Upon collecting a resource, individuals have the opportunity to accumulate “capital” (e.g. grow muscular tissue, build a protective shelter, buy a car, etc.), which eventually increases their productivity and/or their chances of survival. As a result, delaying the collection of a resource creates an opportunity cost in the sense that during the waiting time, the benefits otherwise generated by the increment in capital are lost. These forgone benefits are independent of collection risks and constitute waiting costs per se. Using optimal control theory we show that these costs can lead to the evolution of short time horizons even in the complete absence of collection risks. Moreover, assuming diminishing returns to capital, we show that the evolutionarily stable time horizon increases with the amount of capital already owned by individuals. When individuals possess little capital, they have a lot of room to improve their productivity and/or survival, hence they should be impatient to collect resources; that is, their time horizon should be short. On the contrary, when individuals already possess a lot of capital, the benefits of further accumulation are plateauing, hence patience becomes a more profitable strategy and individuals should lengthen their time horizon. This means that individuals get more patient as they age and that people in deprivation, who still have important productive and survival needs that can be satisfied, should have a shorter time horizon. Moreover, beyond time horizon, our model shows that people with little capital should also be more risk averse than the more privileged. Taken together, these results lead us to interpret the behavioral constellation of deprivation in a new way.