Pandora’s Problem with Deadlines

Pandora’s problem is a fundamental model that studies optimal search under costly inspection. In the classic version, there are n boxes, each associated with a known cost and a known distribution over values. A strategy inspects the boxes sequentially and obtains a utility that equals the difference between the maximum value of an inspected box and the total inspection cost. Weitzman (1979) presented a surprisingly simple strategy that obtains the optimal expected utility. In this work we introduce a new variant of Pandora’s problem in which every box is also associated with a publicly known deadline, indicating the final round by which its value may be chosen. This model captures many real-life scenarios where alternatives admit deadlines, such as candidate interviews and college admissions. Our main result is an efficient threshold-based strategy that achieves a constant approximation relative to the performance of the optimal strategy for the deadlines setting.

Authors

• Ben Berger Offchain Labs, Inc.
• Tomer Ezra Simons Laufer Mathematical Sciences Institute
• Michal Feldman Tel Aviv University Microsoft ILDC
• Federico Fusco Sapienza University of Rome

Keywords

• GTEP: Game Theory
• RU: Decision/Utility Theory
• RU: Sequential Decision Making
• RU: Stochastic Optimization