Pricing Pandora's Boxes: Revenue Maximization in Sequential Information Acquisition

2026-07-25

AI Summary

This study addresses the design of optimal pricing mechanisms for sequential information seekers: a buyer inspects stochastic options one by one following the Pandora’s rule, while a seller commits to non-adaptive prices for value revelations to maximize expected revenue. The authors propose a concise pricing scheme based on equalizing Weitzman indices, achieving a 4-approximation to the optimal revenue under general distributions. They fully characterize the optimal pricing structure in special cases such as identical distributions or monotone hazard rates, and establish tight approximation guarantees in a variant allowing optional inspection. The analysis integrates tools from mechanism design, the Pandora’s box model, and approximation algorithm theory.

Abstract

We study a mechanism design problem in which a seller controls access to information about a set of stochastic alternatives, and a buyer sequentially acquires information in order to choose a single alternative with high value. The value distributions of the alternatives are known to both parties. The seller posts non adaptive prices for revealing each alternative's realized value, and the buyer responds optimally by following a Pandora's Box strategy: deciding which alternatives to inspect and when to stop by accepting the best inspected alternative. The seller's goal is to maximize his expected revenue, i.e. the total payment collected from all inspections. We study the revenue objective through the lens of simplicity versus optimality. Our main result is that a simple and efficiently computable pricing scheme obtains a 4 approximation in the worst case to the optimal revenue. This pricing rule equalizes the Weitzman indices across all alternatives. In contrast, we show that equalizing the prices themselves can be an unbounded factor worse than the optimum. Furthermore, for several natural special cases, including identically distributed alternatives and monotone hazard rate distributions, we fully characterize the optimal pricing. Finally, we also study a variant of our model under optional inspection, where the buyer may select an alternative without observing its realization. In this setting, we obtain an n/(n-1) approximation for the special case of n identically distributed alternatives, as well as a 2 approximation for the special case where each alternative's value distribution has support size two. Overall, our results highlight both the computational challenges and the power of simple pricing schemes in selling information to a sequential searcher.

Problem

• Pandora's Box
• revenue maximization
• sequential information acquisition
• mechanism design
• information pricing

Innovation

• Pandora's Box
• information pricing
• Weitzman index
• revenue maximization
• sequential search