Chapter The Price of Uncertainty in Present-Biased Planning

The tendency to overestimate immediate utility is a common cognitive bias. As a result people behave inconsistently over time and fail
to reach long-term goals. Behavioral economics tries to help affected individuals
by implementing external incentives. However, designing robust
incentives is often difficult due to imperfect knowledge of the parameter
β ∈ (0, 1] quantifying a person’s present bias. Using the graphical model
of Kleinberg and Oren [8], we approach this problem from an algorithmic
perspective. Based on the assumption that the only information about
β is its membership in some set B ⊂ (0, 1], we distinguish between two
models of uncertainty: one in which β is fixed and one in which it varies
over time. As our main result we show that the conceptual loss of effi-
ciency incurred by incentives in the form of penalty fees is at most 2
in the former and 1 + max B/ min B in the latter model. We also give
asymptotically matching lower bounds and approximation algorithms.