In this study, we investigate auctions in two-sided markets with budget constraints on buyers. Our goal is to propose an efficient mechanism that satisfies dominant strategy incentive compatibility (DSIC), individual rationality (IR), and weak budget balance (WBB). To avoid several known impossibility theorems for each of two-sided markets and budget constraints, we assume prior information on sellers' valuations and investigate the efficiency of mechanisms by means of liquid welfare (LW), an efficiency measure used for budget-constrained auctions, in addition to social welfare (SW). Our first result is to improve the efficiency guarantees of the Polyhedral Clinching Auction by Hirai and Sato (2022), proposed for two-sided markets in which each seller is assumed to be truthful. We show that even under budget constraints and polymatroid constraints, their mechanism achieves an LW of more than 1/2 of the optimal LW, and an SW of more than the optimal LW. This significantly strengthens the efficiency guarantees of the existing studies on clinching auctions. Our second result is the extension of the Polyhedral Clinching Auction to a single-sample mechanism. Under the assumption that a single sample is provided from each seller's distribution on her valuation, we utilize the first result and propose an efficient mechanism that satisfies DSIC, IR, and WBB. Our mechanism achieves an LW of more than 1/4 of the optimal LW, and an SW of more than 1/2 of the optimal LW, in expectation. This result can be viewed as a budget extension of D"{u}tting et al. (2021).

翻译：本研究探究了买方存在预算约束的双边市场拍卖机制。我们的目标是提出一种满足占优策略激励相容（DSIC）、个体理性（IR）与弱预算平衡（WBB）的高效机制。为避免双边市场与预算约束各自存在的若干已知不可能性定理，我们假设卖方估值的先验信息，并以流动性福利（LW）（一种用于预算约束拍卖的效率度量）与社会福利（SW）作为机制效率的评估标准。首个成果是改进了Hirai与Sato（2022）提出的多面体式渐进拍卖的效率保证——该机制原适用于假设每位卖方诚实报价的双边市场。我们证明：即便在预算约束与多拟阵约束下，该机制的LW仍能达到最优LW的1/2以上，SW则超过最优LW。这显著强化了现有渐进拍卖研究的效率保证。第二个成果是将多面体式渐进拍卖扩展为单样本机制。在假设获得每位卖方估值分布的单个样本后，我们利用首个成果提出满足DSIC、IR与WBB的高效机制。从期望值看，该机制的LW超过最优LW的1/4，SW超过最优LW的1/2。这一结果可视为Dütting等人（2021）的预算约束扩展。