A Bounded Rationality Approach to β, δ Preferences

Borrowing from Cognitive Heierarchy Theory, I introduce bounded rationality into the β, δ 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. The k-2–sophisticate does one round of strategic thinking about her future behavior instead of the unlimited number of rounds of the usual sophisticate. In the “doing it once” model of procrastination of O’Donoghue and Rabin (1999) the k-2–sophisticate typically procrastinates and preproperates less than the full sophisticate, and is protected from severe harm from both extreme preproperation and extreme procrastination, though she may suffer from excessive costly preemption due to pessimism about future preemption when costs are immediate.