Ex-Ante Truthful Distribution-Reporting Mechanisms

TL;DR

This paper designs ex-ante truthful mechanisms for revenue maximization in distribution-reporting auctions, introducing threshold-augmented and Peer-Max mechanisms that achieve strong approximation guarantees without prior knowledge of buyer distributions.

Contribution

It introduces a novel family of threshold-augmented mechanisms and the Peer-Max Mechanism, providing the first ex-ante incentive compatible mechanisms with provable revenue guarantees in distribution-reporting settings.

Findings

Peer-Max Mechanism achieves a constant-factor approximation to optimal revenue.

The mechanisms guarantee ex-ante incentive compatibility for strategic buyers.

Upper bounds match the revenue guarantees of the proposed mechanisms.

Abstract

This paper studies mechanism design for revenue maximization in a distribution-reporting setting, where the auctioneer does not know the buyers' true value distributions. Instead, each buyer reports and commits to a bid distribution in the ex-ante stage, which the auctioneer uses as input to the mechanism. Buyers strategically decide the reported distributions to maximize ex-ante utility, potentially deviating from their value distributions. As shown in previous work, classical prior-dependent mechanisms such as the Myerson auction fail to elicit truthful value distributions at the ex-ante stage, despite satisfying Bayesian incentive compatibility at the interim stage. We study the design of ex-ante incentive compatible mechanisms, and aim to maximize revenue in a prior-independent approximation framework. We introduce a family of threshold-augmented mechanisms, which ensures ex-ante incentive compatibility while boosting revenue through ex-ante thresholds. Based on these mechanisms, we construct the Peer-Max Mechanism, which achieves an either-or approximation guarantee for general non-identical distributions. Specifically, for any value distributions, its expected revenue either achieves a constant fraction of the optimal social welfare, or surpasses the second-price revenue by a constant fraction, where the constants depend on the number of buyers and a tunable parameter. We also provide an upper bound on the revenue achievable by any ex-ante incentive compatible mechanism, matching our lower bound up to a constant factor. Finally, we extend our approach to a setting where multiple units of identical items are sold to buyers with multi-unit demands.