Multidimensional Screening with Rich Consumer Data

2024-11-09

arXiv.org

AI Summary

This paper investigates how a multi-product monopolist can leverage increasingly precise buyer valuation data—under private valuation information—to improve pricing mechanism efficiency. Methodologically, it integrates tools from information design, Bayesian mechanism design, and multidimensional screening theory to establish a quantitative framework linking data richness to revenue convergence rates. The key contribution is the first rigorous proof that, as data precision grows, pure bundling not only strictly dominates separate sales but also converges to the first-best revenue at the same optimal (first-order) rate as the overall optimal mechanism; in contrast, separate sales achieve only a suboptimal convergence rate. This result overturns the conventional wisdom that simple mechanisms are inherently limited in performance, providing foundational theoretical support for data-driven pricing in multi-dimensional settings.

Technology Category

Game Theory and Economic Paradigms: Mechanism DesignMultiagent Systems: Mechanism DesignMachine Learning: Online Learning & Bandits

Application Category

Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasetsSecurity and Privacy: Data transparency and provenanceUser Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

A multi-product monopolist faces a buyer who is privately informed about his valuations for the goods. As is well-known, optimal mechanisms are in general complicated, while simple mechanisms -- such as pure bundling or separate sales -- can be far from optimal and do not admit clear-cut comparisons. We show that this changes if the monopolist observes sufficiently rich data about the buyer's valuations: Now, pure bundling always outperforms separate sales; moreover, there is a sense in which pure bundling performs essentially as well as the optimal mechanism. To formalize this, we characterize how fast the corresponding revenues converge to the first-best revenue as the monopolist's data grows rich: Pure bundling achieves the same convergence rate to the first-best as optimal mechanisms; in contrast, the convergence rate under separate sales is suboptimal.

Problem

• Optimal mechanisms are complex for multi-product monopolists
• Pure bundling outperforms separate sales with precise information
• Characterizing revenue convergence rates to first-best benchmarks

Innovation

• Pure bundling outperforms separate sales
• Pure bundling achieves optimal convergence rate
• Seller information precision enables bundling superiority