Abstract
We study a generalized Pandora's box problem Weitzman (1979) in which boxes could be either (fully) opened for a certain fee to reveal their exact prizes, or partially opened at a reduced cost prior to being fully opened. This feature introduces a tradeoff where on one hand, partial opening provides a more accurate estimation of the box's prize without commitment to full opening, but on the other hand, overusing the option of partial opening may lead to excessive costs. We employ an array of techniques that were used to analyze related problems to provide a comprehensive analysis which includes (1) the identification of structural properties of the optimal policy that provide insights into what drives optimal opening decisions; (2) the derivation of provably near-optimal solutions to the stochastic and online problems; and (3) an extensive numerical study designed to examine the practical effectiveness of our policies. We find that while in general, characterizing the optimal policy is difficult, certain intuitive threshold-based policies that extend Pandora's box solution are extremely effective in solving our generalized problem.
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