Robust Mechanism Design with Anonymous Information

2026-02-24

AI Summary

This study addresses the design of robust auction mechanisms that maximize worst-case expected revenue when only anonymous and endogenously truncated order statistics—such as ranked bids in auctions—are observed. Focusing on the class of symmetric monotone mechanisms, the paper integrates robust optimization, mechanism design theory, and inference from order statistics to establish that canonical mechanisms—including uniform pricing, Myerson’s optimal auction, and second-price auctions with reserve prices—achieve worst-case revenue optimality under this informational constraint. The findings reveal that fairness and privacy protection can naturally emerge from the anonymity inherent in the observed data structure. The results are further extended to generalized settings, including multi-item and position auctions.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Security and Privacy: Large-scale security measurements

Abstract

In practice, auction data are often endogenously censored and anonymous, revealing only limited outcome statistics rather than full bid profiles. We study robust auction design when the seller observes only aggregated, anonymous order statistics and seeks to maximize worst-case expected revenue over all product distributions consistent with the observed statistic. We show that simple and widely used mechanisms are robustly optimal. Specifically, posted pricing is robustly optimal given the distribution of the highest value; the Myerson auction designed for the unique consistent i.i.d. distribution is robustly optimal given the lowest value distribution; and the second-price auction with an optimal reserve is robustly optimal when an intermediate order statistic is observed and the implied i.i.d. distribution is regular above its reserve. More generally, for a broad class of monotone symmetric mechanisms depending only on the top k order statistics, including multi-unit and position auctions, the worst-case revenue is attained under the i.i.d. distribution consistent with the observed k-th order statistic. Our results provide a tractable foundation for non-discriminatory auction design, where fairness and privacy are intrinsic consequences of the information structure rather than imposed constraints.

Problem

• robust mechanism design
• anonymous information
• auction design
• order statistics
• worst-case revenue

Innovation

• robust mechanism design
• anonymous information
• order statistics
• worst-case revenue
• non-discriminatory auctions