具有ROI约束投标者的拍卖设计：真实性（Truthfulness）与收益最大化
Auction Design with ROI-Constrained Bidders: Truthfulness and Revenue Maximization
- Qiannan Normal University for Nationalities（黔南民族师范学院）
- Guizhou University（贵州大学）
- Griffith University（格里菲斯大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对ROI约束投标者，刻画真实拍卖特征，提出σ-增量机制渐近最优并保证收益比例，单投标者情形下以凸定价函数实现最优。
AI中文摘要：
投资回报率（ROI）约束在许多拍卖中至关重要，尤其是在在线广告中，投标者不愿支付超过所获价值固定比例的价格。我们研究针对具有ROI约束投标者的真实且收益最大化的拍卖。我们首先刻画了当估值和ROI约束均为私有信息时的真实拍卖，表明分配规则唯一地决定了支付规则。基于这一刻画，对于多个投标者，我们引入了σ-增量机制，该机制类似于Myerson的最优机制；当σ趋近于零时，这些机制在确定性真实机制中渐近最优，且其收益至少达到所有真实机制最优期望收益的1/$\bar r$比例，其中$\bar r$是最大的可能ROI约束。在单投标者情形下，我们证明每个真实拍卖都可以被一个凸定价函数替代，该函数对每种类型产生弱更高的支付，并且当估值或ROI约束为公开信息时，我们推导出最优定价函数。
英文摘要：
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.
