It Is Time to Get Some Rest

Abstract

We introduce the fatigue disutility model. Set in continuous time, the model formalizes the notion that fatigue accumulates with effort, decays with rest, and produces an increase in marginal instant disutility. The model is meant to be prescriptive, although it rationalizes several anomalies observed in time preference. Under very general conditions, the most efficient temporal profile of effort exhibits a high-low-high pattern. We consider a variant whereby marginal productivity decreases with fatigue, and we examine the optimal management of fatigue and productivity under various scenarios. We also reexamine the beneficial role of breaks in reducing fatigue. We bring the model to the data and provide a calibration that favorably predicts the speed profiles observed in swimming competitions. Data are available at https://doi.org/10.1287/mnsc.2017.3018 . This paper was accepted by Han Bleichrodt, decision analysis.