Procrastination with variable present bias

TL;DR

This paper studies how variable present bias affects procrastination, revealing conditions under which procrastination becomes exponentially severe or remains bounded, using a novel connection to optimal pricing theory.

Contribution

It introduces a model where present bias varies over time and characterizes the worst-case procrastination ratios using a new connection to pricing theory.

Findings

Worst-case procrastination ratio can be exponential or constant depending on bias distribution.

Identifies task graph structures that mitigate procrastination.

Provides conditions for bounded and unbounded procrastination ratios.

Abstract

Individuals working towards a goal often exhibit time inconsistent behavior, making plans and then failing to follow through. One well-known model of such behavioral anomalies is present-bias discounting: individuals over-weight present costs by a bias factor. This model explains many time-inconsistent behaviors, but can make stark predictions in many settings: individuals either follow the most efficient plan for reaching their goal or procrastinate indefinitely. We propose a modification in which the present-bias parameter can vary over time, drawn independently each step from a fixed distribution. Following Kleinberg and Oren (2014), we use a weighted task graph to model task planning, and measure the cost of procrastination as the relative expected cost of the chosen path versus the optimal path. We use a novel connection to optimal pricing theory to describe the structure of the worst-case task graph for any present-bias distribution. We then leverage this structure to derive conditions on the bias distribution under which the worst-case ratio is exponential (in time) or constant. We also examine conditions on the task graph that lead to improved procrastination ratios: graphs with a uniformly bounded distance to the goal, and graphs in which the distance to the goal monotonically decreases on any path.