Procrastination, self-imposed deadlines and other commitment devices

In this paper we model a decision maker who must exert costly effort to complete a single task by a fixed deadline. Effort costs evolve stochastically in continuous time. The decision maker will then optimally wait to exert effort until costs are less than a given threshold, the solution to an optimal stopping time problem. We derive the solution to this model for three cases: (1) time consistent decision makers, (2) naıve hyperbolic discounters and (3) sophisticated hyperbolic discounters. Sophisticated hyperbolic discounters behave as if they were time consistent but instead have a smaller reward for completing the task. We show that sophisticated decision makers will often self-impose a deadline to ensure early completion of the task. Other forms of commitment are also discussed.