The Pandora's Box Problem with Sequential Inspections

2025-07-10

AI Summary

This paper studies an extended Pandora’s box problem under sequential inspection, focusing on a novel information–cost trade-off where an agent chooses between “full inspection” (yielding exact values at high cost) and “partial inspection” (yielding coarse-grained information at low cost). We propose a threshold-based approximately optimal search policy, characterize its structural properties for the first time, and derive closed-form optimal solutions for nontrivial special cases—overcoming the classical model’s limitation to binary (full/no) information acquisition. Using stochastic optimization modeling, Lagrangian relaxation, and numerical analysis, we obtain near-optimal policies with theoretical performance guarantees. Experiments demonstrate substantial improvements in cost efficiency, systematically revealing the interplay between information granularity and search cost. Our work broadens both the theoretical foundations and practical applicability of the Pandora’s box framework.

Technology Category

• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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 establish a hardness result and employ an array of techniques in stochastic optimization to provide a comprehensive analysis of this model. This 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; (3) the characterization of the optimal policy in special yet non-trivial cases; and (4) an extensive numerical study that compares the performance of various policies, and which provides additional insights about the optimal policy. Throughout, we show that intuitive threshold-based policies that extend the Pandora's box optimal solution can effectively guide search decisions.

Problem

• Generalizes Pandora's box problem with partial inspections
• Balances information acquisition and cost efficiency tradeoffs
• Analyzes optimal policies via stochastic optimization techniques

Innovation

• Sequential inspections with partial and full openings
• Stochastic optimization for near-optimal solutions
• Threshold-based policies guiding optimal search decisions