A Bounded Rationality Approach to Beta-Delta Preferences

Borrowing from Cognitive Hierarchy Theory, I introduce bounded rationality into the beta-delta model of present-biased preferences. I define a level-two agent–or k-2 sophisticate–as one who is aware that her future selves will have present-bias, but believes that they will be naive about their future present-bias. The key feature of the k-2 sophisticate is that she does only one round of backwards induction about her future behavior instead of the unlimited number of rounds of the full sophisticate. Extending the framework of O’Donoghue and Rabin, 1999, in which an agent must take an action exactly one time in a finite period of time, the k-2 sophisticate always procrastinates tasks with immediate costs less than the full sophisticate, and almost always preproperates (does too soon) tasks with immediate rewards less than the full sophisticate. In addition, the k-2 sophisticate is protected from severe harm from both extreme preproperation and extreme procrastination, overcoming one of the intuitively implausible results of the O’Donoghue and Rabin model. There are cases in which the k-2 sophisticate may suffer from excessive costly preemption of future procrastinatin due to incorrect pessimism about future preemption, which I argue is not impluasible. My model also overcomes the dissatisfying result from O’Donoghue and Rabin (2001) that in an infinite-horizon setting it is not possible to identify when the fully sophisticated individual will actually do the task.