Robust Mechanism Design with Anonymous Information

TL;DR

This paper investigates robust auction design when only anonymous, aggregated outcome data is available, identifying mechanisms that maximize worst-case revenue under limited information.

Contribution

It characterizes the optimality of simple auction mechanisms under anonymous data and develops a framework for robust, non-discriminatory auction design based on limited statistics.

Findings

Posted pricing is optimal given the highest value distribution.

Myerson auction is optimal for the lowest value distribution.

Second-price auction with reserve is optimal for intermediate order statistics.

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.