发表机构
University of Amsterdam; Centrum Wiskunde & Informatica (CWI); Technical University of Munich（阿姆斯特丹大学; 数学与计算机科学中心; 慕尼黑工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过线性规划对偶框架，为带预算约束的多种拍卖格式推导出紧致的流动性福利无政府状态价格界，并匹配了统一价格拍卖的已知上界。
AI 中文摘要
我们研究了具有预算约束投标人的拍卖效率，并推导了粗相关均衡（CCE）的紧致无政府状态价格（PoA）界。为此，我们开发了一个通用框架，将证明PoA保证简化为寻找线性规划对偶的可行解。该线性规划基于每个投标人的少量均衡统计量构建，纳入了拍卖设置和均衡行为所隐含的约束，并捕捉了一种针对预算受限环境定制的新平滑性概念；我们提供了从经典平滑性到这一新概念的归约。我们的方法使得在广泛的拍卖格式中能够进行简单且紧致的PoA分析。利用我们的框架，我们获得了同步一价拍卖、二价拍卖和全支付拍卖，具有受限统一投标接口的同步拍卖，歧视性和统一价格多单位拍卖，以及广义一价位置拍卖的紧致流动性福利保证。在预算受限设置之外，我们为无预算统一价格拍卖和广义二价拍卖推导了新的下界；特别是，我们对统一价格拍卖的下界与de Keijzer等人（2013）的$3.146$上界相匹配。
英文摘要
We study the efficiency of auctions with budget-constrained bidders and derive tight price of anarchy (PoA) bounds for coarse correlated equilibria (CCE). To this end, we develop a general framework that reduces proving PoA guarantees to finding feasible solutions to the dual of a linear program. The LP is formulated over a small number of per-bidder equilibrium statistics, incorporates constraints implied by the auction setting and equilibrium behavior, and captures a novel smoothness notion tailored to budget-constrained environments; we provide a reduction from classical smoothness to this new notion. Our approach enables simple and tight PoA analyses across a broad range of auction formats. Using our framework, we obtain tight liquid welfare guarantees for simultaneous first-price, second-price, and all-pay auctions, simultaneous auctions with restricted uniform bidding interfaces, discriminatory and uniform price multi-unit auctions, and generalized first-price position auctions. Beyond budget-constrained settings, we derive new lower bounds for the budget-free uniform price auction and generalized second-price auction; in particular, our lower bound for the uniform price auction matches the upper bound of $3.146$ by de Keijzer et al. (2013).
