The Pandora's Box Problem with Sequential Inspections

Abstract

The Pandora's box problem (Weitzman 1979) 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 problem relaxations and provably near-optimal solutions; 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 can effectively guide search decisions.

Keywords: pandora's box problem, dynamic programming, approximate algorithms