Anonymous Pricing in Large Markets

2026-01-23

AI Summary

This study addresses the revenue performance of anonymous pricing in multi-unit auctions with ex ante heterogeneous unit-demand buyers. Under (quasi-)regularity assumptions and leveraging tools from mechanism design theory, the paper employs approximation and asymptotic analysis to characterize revenue guarantees in large markets. The main contribution is a tight bound showing that anonymous pricing achieves a $2 + O(1/\sqrt{k})$-approximation to the optimal revenue, where $k$ denotes the number of units. In the worst case—when $k = 1$—this ratio is approximately 2.47, and it converges to 2 as $k$ grows. These results imply that the revenue gain from third-degree price discrimination is limited in large markets, thereby challenging the conventional pessimism regarding the efficacy of anonymous pricing.

Technology Category

• Game Theory and Economic Paradigms: Auctions and Market-Based Systems
• Multiagent Systems: Mechanism Design
• Machine Learning: Privacy

Application Category

• Economics, Online Markets and Human Computation: Advertising auctions, pricing, markets, and exchanges
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

We study revenue maximization when a seller offers $k$ identical units to ex ante heterogeneous, unit-demand buyers. While anonymous pricing can be $\Theta(\log k)$ worse than optimal in general multi-unit environments, we show that this pessimism disappears in large markets, where no single buyer accounts for a non-negligible share of optimal revenue. Under (quasi-)regularity, anonymous pricing achieves a $2+O(1/\sqrt{k})$ approximation to the optimal mechanism; the worst-case ratio is maximized at about $2.47$ when $k=1$ and converges to $2$ as $k$ grows. This indicates that the gains from third-degree price discrimination are mild in large markets.

Problem

• anonymous pricing
• revenue maximization
• large markets
• price discrimination
• multi-unit auctions

Innovation

• anonymous pricing
• large markets
• revenue maximization
• price discrimination
• multi-unit auctions