Auction Design with ROI-Constrained Bidders: Truthfulness and Revenue Maximization

2026-09-14

AI Summary

研究了ROI约束下竞拍者的真实性和收益最大化拍卖设计，提出σ-增量机制接近最优收益。

Abstract

The return-on-investment (ROI) constraint is central to many auctions, particularly in online advertising, where a bidder is unwilling to pay more than a fixed fraction of the value obtained. We study truthful and revenue-maximizing auctions for ROI-constrained bidders. We first characterize truthful auctions when both valuations and ROI constraints are private, showing that the allocation rule uniquely determines the payment rule. Building on this characterization, for multiple bidders we introduce $σ$-increment mechanisms that resemble Myerson's optimal mechanism~\cite{journals/mor/Myerson81}; as $σ$ vanishes, these mechanisms become asymptotically optimal among deterministic truthful mechanisms, and their revenue approaches at least a $1/\bar r$ fraction of the optimal expected revenue over all truthful mechanisms, where $\bar r$ is the largest possible ROI constraint. In the single-bidder setting, we prove that every truthful auction can be replaced by a convex pricing function with weakly higher payments for every type, and we derive the optimal pricing functions when either the valuation or the ROI constraint is public.

Problem

• Auction Design
• ROI Constraint
• Truthfulness
• Revenue Maximization

Innovation

• truthful auctions
• ROI-constrained bidders
• σ-increment mechanisms
• revenue maximization