Abstract
The Pandora’s box problem is a core model in economic theory that captures an agent’s (Pandora’s) search for the best alternative (box). We study an important generalization of the problem where the agent can either fully open boxes for a certain fee to reveal their exact values or partially open them at a reduced cost. This introduces a new tradeoff between information acquisition and cost efficiency. We employ an array of techniques in stochastic optimization to provide a comprehensive analysis of this model, which includes (1) the identification of structural properties of the optimal policy that provide insights about optimal decisions; (2) the derivation of provably near-optimal solutions to offline and online variants of the problem; and (3) an extensive numerical study that compares various policies and provides additional insights. Throughout, we show that intuitive threshold-based policies that extend the Pandora’s box optimal solution provide very effective solutions.