On the Value of Penalties in Time-Inconsistent Planning

People tend to behave inconsistently over time due an inherent present bias. As this may impair performance, social and economic settings need be adapted accordingly. Common tools reduce the impact of time-inconsistent behavior are penalties prohibition. Such called commitment devices. In recent work Kleinberg Oren [6, 7] connect design prohibition-based devices a combinatorial problem in which edges removed from task graph G with n nodes. However, is NP-hard approximate within ratio less than √n/3 [2]. To address issue, we propose penalty-based device that does not delete but raises their cost. The benefits our approach twofold. On conceptual side, show up 1/β times more efficient prohibition, where β ϵ (0,1] parameterizes computational significantly improve approximability by presenting 2-approximation algorithm for allocating penalties. complement result, prove optimal 1.08192.