We address auctions in two-sided markets with budget constraints on buyers, a fundamental setting also crucial for applications such as display advertising. Our goal is to design efficient mechanisms that satisfy dominant strategy incentive compatibility, individual rationality, and budget balance. To overcome the limitations of impossibility theorems, we assume prior knowledge of sellers' valuations and focus on liquid welfare, an efficiency objective that takes budgets into account. Our contributions are twofold: First, we improve the efficiency guarantees of the polyhedral clinching auction by Hirai and Sato (2022). Second, using the reduction method of D"{u}tting et al. (2021), we extend the mechanism to an efficient single-sample mechanism for budget-constrained auctions, providing the budget extension of their results. Notably, our results hold even under polymatroid constraints and apply to both divisible and indivisible goods.

翻译：本文研究买卖双方市场中买家存在预算约束的拍卖问题，这一基础设定对展示广告等应用场景至关重要。我们的目标是设计满足占优策略激励相容性、个体理性与预算平衡的高效机制。为克服不可能性定理的限制，我们假设已知卖方估值的先验分布，并聚焦于考虑预算约束的流动性福利这一效率目标。我们的贡献主要体现在两个方面：首先，我们改进了Hirai和Sato（2022）提出的多面体锁定拍卖的效率保证。其次，基于D"{u}tting等人（2021）的归约方法，我们将该机制扩展为适用于预算约束拍卖的高效单样本机制，从而实现了其结论在预算约束下的推广。值得注意的是，我们的结果即使在多拟阵约束下依然成立，并且同时适用于可分商品与不可分商品。