We study the setting of welfare maximization in bilateral trade, where the values of both the buyer and the seller are drawn from independent distributions. Our goal is to maximize social welfare. In this setting, fixed price mechanisms have been extensively studied. In a fixed price mechanism, there is a price $p$ that depends only on the distributions of the buyer and the seller. Trade occurs if and only if the buyer's value is at least $p$ and the seller's value is at most $p$. A long line of work has culminated in determining almost exactly the approximation ratios achievable by fixed price mechanisms: there exists a fixed price mechanism that obtains at least a $0.72$ fraction of the social welfare, but no fixed price mechanism can guarantee more than a $0.7381$ fraction of it [Cai and Wu, STOC'23; Liu, Ren, and Wang, STOC'23]. No other incentive-compatible mechanism is known to beat the performance of fixed-price mechanisms in this setting. This paper shows how to achieve a larger fraction of the optimal welfare with other classes of mechanisms. Specifically, we study the buyer-offering mechanism with a reserve price. In this mechanism, the buyer observes its value and makes a take-it-or-leave-it offer to the seller, where the offer is at least the reserve price. Beyond its simplicity, this natural mechanism is attractive because the seller always has a dominant strategy: accept the offer if its value is at most the offer, and otherwise reject it. We show that there always exists a reserve price that guarantees a $0.746$ fraction of the social welfare. This not only improves upon the best previously known approximation guarantee for the problem, but also demonstrates that fixed-price mechanisms are not optimal in this setting.

翻译：我们研究了双边贸易中的福利最大化问题，其中买方和卖方的价值均从独立分布中抽取。我们的目标是最大化社会福利。在此背景下，固定价格机制已被广泛研究。在固定价格机制中，存在一个仅取决于买方和卖方分布的价格$p$，当且仅当买方价值不低于$p$且卖方价值不高于$p$时交易发生。一系列研究最终几乎精确确定了固定价格机制所能实现的近似比：存在一个固定价格机制可获得至少$0.72$倍的社会福利，但没有任何固定价格机制能保证超过$0.7381$倍的社会福利 [Cai and Wu, STOC'23; Liu, Ren, and Wang, STOC'23]。在该问题中，尚未发现其他激励相容机制能超越固定价格机制的性能。本文展示了如何通过其他类别的机制实现更大比例的最优福利。具体来说，我们研究了带保留价的买方报价机制。在该机制中，买方根据自身价值向卖方发出"接受或放弃"的报价，且该报价至少为保留价。除简洁性外，这种自然机制的吸引力在于卖方始终具有占优策略：若其价值不超过报价则接受，否则拒绝。我们证明总存在一个保留价能保证$0.746$倍的社会福利。这不仅改进了该问题此前已知的最佳近似保证，也表明固定价格机制在该场景下并非最优。