招募较小一侧的力量：在双边市场中额外两名交易者即足够

中文摘要 AI 辅助

我们研究了双边双向拍卖中Bulow-Klemperer风格的竞争复杂度，其中有$m$个单位需求的买家，独立同分布地来自分布$F_B$，以及$n$个单位供给的卖家，独立同分布地来自分布$F_S$。当$m \ge n$且买家估值一阶随机占优于卖家成本（$F_B \succeq_{\mathrm{FSD}} F_S$）时，我们证明仅招募两名额外卖家即可使卖家贸易削减（STR）这一先验无关机制实现至少等于原始市场最优贸易收益（GFT）的期望GFT。当买家侧是市场的较小一侧（$m \le n$）时，对买家贸易削减（Buyer Trade Reduction）在额外招募两名买家的情况下也有类似结果。这解决了Babaioff、Goldner和Gonczarowski（SODA 2020）以及Cai、Liaw、Mehta和Zhao（STOC 2024）的开放问题。我们通过证明该统一上界是最优的来补充我们的上界：即使在$m = n = 1$的情况下，任何无先验机制（确定性的或随机化的），只要满足占优策略激励相容、个体理性和弱预算平衡，都无法通过仅招募一名额外卖家来匹配最优GFT。

英文摘要

We study Bulow-Klemperer-style competition complexity in two-sided double auctions with $m$ unit-demand buyers drawn i.i.d. from $F_B$ and $n$ unit-supply sellers drawn i.i.d. from $F_S$. When $m \ge n$ and buyer valuations first-order stochastically dominate seller costs ($F_B \succeq_{\mathrm{FSD}} F_S$), we prove that recruiting just two additional sellers enables Seller Trade Reduction (STR), a prior-independent mechanism, to achieve expected Gains From Trade (GFT) at least the first-best GFT of the original market. When the buyer side is the smaller side of the market ($m \le n$), an analogous result holds for Buyer Trade Reduction with 2 additional buyers. This resolves open questions of Babaioff, Goldner, and Gonczarowski (SODA 2020) and Cai, Liaw, Mehta, and Zhao (STOC 2024). We complement our upper bound by showing that this uniform bound is optimal: already for $m = n = 1$, no prior-free mechanism (deterministic or randomized) that is dominant-strategy incentive-compatible, individually rational, and weakly budget-balanced can match the first-best GFT by recruiting only one additional seller.

发表机构

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

机构由 AI 辅助整理，请以论文原文为准。