Stochastic Procrastination and Optimal Task Division

Abstract

Procrastination is widespread, costly, and persistent despite strong intentions to change. We show how procrastination can arise in stationary environments, where there are no deadlines, changing incentives, or new information to justify delay. With hyperbolic discounting, stochastic delay, i.e., acting with a fixed probability each period, emerges as the only self‑consistent policy: the only policy that resolves belief-policy inconsistency. We further show that standard reinforcement learning algorithms converge to this Pareto-inefficient solution. We extend the self-consistent model to divisible and continuous-action tasks. In these settings, allowing a voluntary break after completing a subtask never increases, and often reduces, expected delay; enforcing such breaks can reduce delay further, often substantially. Optimal task division equalizes completion probabilities across subtasks, implying that early stages of a larger task should be easier when the goal is to reduce overall time to completion. The model therefore gives a formal rationale and exact quantification for familiar remedies such as task division, starting easy, and enforced breaks, while explaining why procrastination can persist even when intentions, incentives, and information remain unchanged.