In many settings, 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 graph-theoretic model of tasks and goals, in which dependencies among actions are represented by a directed graph, and 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 motivate agents to reach designated goals.
A fundamental issue in behavioral economics—and in the modeling of individual decision-making more generally—is to understand the effects of decisions that are inconsistent over time. Examples of such inconsistency are widespread in everyday life: we make plans for completing a task but then procrastinate; we put work into getting a project partially done but then abandon it; we pay for gym memberships but then fail to make use of them. In addition to analyzing and modeling these effects, there has been increasing interest in incorporating them into the design of policies and incentives in domains that range from health to personal finance.
These types of situations have a recurring structure: a person makes a plan at a given point in time for something they will do in the future (finishing homework, exercising, paying off a loan), but at a later point in time they fail to follow through on the plan. Sometimes this failure is the result of unforeseen circumstances that render the plan invalid—a person might join a gym but then break their leg and be unable to exercise—but in many cases the plan is abandoned even though the circumstances are essentially the same as they were at the moment the plan was made. This presents a challenge to any model of planning based on optimizing a utility function that is consistent over time: in an optimization framework, the plan must have been an optimal choice at the outset, but later it was optimal to abandon it. A line of work in the economics literature has thus investigated the properties of planning with objective functions that vary over time in certain natural and structured ways.
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