广义比例一级价格拍卖在自动出价下的效率

中文摘要 AI 辅助

自动出价现已被在线广告平台广泛采用，允许广告主设定高层次的营销活动目标——例如在回报支出（ROS）约束下最大化总价值——而非手动逐次出价。算法机制设计中的一个核心问题是刻画在这种无先验（prior-free）环境下，不同拍卖格式的最坏情况效率损失，即无政府价格（Price of Anarchy, PoA）。虽然已知随机拍卖在两名竞拍者情形下比确定性机制严格提高了效率，但两个基本问题仍然悬而未决：（1）两名竞拍者的最优PoA是多少，（2）是否存在任何机制能突破一般n≥3名竞拍者的2屏障？我们利用r-比例一级价格拍卖（pFPA_r）家族解决了这两个问题，其中每个竞拍者以与其出价的r次方（r>0）成比例的概率获胜，并在获胜时支付其出价。首先，对于两名竞拍者，我们证明标准比例一级价格拍卖（r=1）实现了紧致的PoA≤1.5，并辅以匹配的下界，表明任何匿名、单调机制都无法做得更好。其次，对于一般n≥2名竞拍者，设置r=2n可在所有非支配出价配置下实现PoA≤2-1/(4n+1)=2-Ω(1/n)，突破了每个有限n的确定性2屏障，并渐近匹配已知的2-Θ(1/n)下界。

英文摘要

Auto-bidding is now widely adopted in online advertising platforms, allowing advertisers to specify high-level campaign objectives--such as maximizing total value subject to a return-on-spend (ROS) constraint--rather than manual per-query bids. A central question in algorithmic mechanism design is characterizing the worst-case efficiency loss, or Price of Anarchy (PoA), across auction formats in this prior-free setting. While randomized auctions are known to strictly improve efficiency over deterministic mechanisms for two bidders, two fundamental questions have remained open: (1) what is the optimal PoA for two bidders, and (2) can any mechanism beat the barrier of 2 for general $n \ge 3$ bidders? We resolve both questions using the family of $r$-proportional first-price auctions ($\text{pFPA}_r$), in which each bidder wins with probability proportional to their bid raised to an exponent $r > 0$ and pays their bid upon winning. First, for two bidders, we prove that the standard proportional first-price auction ($r = 1$) achieves a tight $\text{PoA} \le 1.5$, complemented by a matching lower bound showing that no anonymous, monotone mechanism can do better. Second, for general $n \ge 2$ bidders, setting $r = 2n$ achieves $\text{PoA} \le 2 - \frac{1}{4n+1} = 2 - Ω(1/n)$ across all undominated bid profiles, breaking the deterministic barrier of 2 for every finite $n$ and asymptotically matching the known $2 - Θ(1/n)$ lower bound.

发表机构

• Yale University（耶鲁大学）
• Google DeepMind（谷歌DeepMind）
• Google Research（谷歌研究院）

机构由 AI 辅助整理，请以论文原文为准。