Long-Range Planning with Time-Inconsistency: A Class of Computational Problems in Behavioral Economics

There are many settings where people set long-range goals and make plans to achieve them. Such long-range planning is becoming an integral of the experience in many on-line contexts, where for example people work toward reputational milestones in question-answering sites, build up to administrative roles in open-source authoring domains, and reach educational goals in on-line learning communities.

In order to understand these kinds of processes, we need to enrich our models with the types of human behavioral biases that come into play when people attempt to reach long-range goals. One of the most fundamental among these is the notion that people exhibit behavior that is inconsistent across time — we allocate a block of time to get work done and then procrastinate, or put effort into a project and then later fail to complete it. An active line of research in behavioral economics and related fields has developed and analyzed models for this type of time-inconsistent behavior.

Here we propose a model in which tasks and goals are represented by a directed graph capturing dependencies, and a a time-inconsistent agent constructs a path through this graph. We first show how instances of this path-finding problem on different input graphs can reconstruct a wide range of qualitative phenomena observed in the literature on time-inconsistency, including procrastination, abandonment of long-range tasks, and the benefits of reduced sets of choices. We then explore a set of analyses that quantify over the set of all graphs; among other results, we find that in any graph, there can be only polynomially many distinct forms of time-inconsistent behavior; and any graph in which a time-inconsistent agent incurs significantly more cost than an optimal agent must contain a large “procrastination” structure as a minor. Finally, we use this graph-theoretic model to explore ways in which tasks can be designed to help motivate agents to reach designated goals.

This is joint work with Sigal Oren.