A truthful mechanism for a Bayesian single-item auction results with some ex-ante revenue for the seller, and some ex-ante total surplus for the buyers. We study the Pareto frontier of the set of seller-buyers ex-ante utilities, generated by all truthful mechanisms when buyers values are sampled independently and identically (i.i.d.). We first provide a complete structural characterization of the Pareto frontier under natural distributional assumptions. For example, when valuations are drawn i.i.d. from a distribution that is both regular and anti-MHR, every Pareto-optimal mechanism is a second-price auction with a reserve no larger than the monopoly reserve. Building on this, we interpret the problem of picking a mechanism as a two-sided bargaining game, and analyze two canonical Pareto-optimal solutions from cooperative bargaining theory: the Kalai-Smorodinsky (KS) solution, and the Nash solution. We prove that when values are drawn i.i.d. from a distribution that is both regular and anti-MHR, in large markets both solutions yield near-optimal welfare. In contrast, under worst-case MHR distributions, their performance diverges sharply: the KS solution guarantees one-half of the optimal welfare, while the Nash solution might only achieve an arbitrarily small fraction of it. These results highlight the sensitivity of fairness-efficiency tradeoffs to distributional structure, and affirm the KS solution as the more robust notion of fairness for asymmetric two-sided markets.

翻译：贝叶斯单物品拍卖的真实机制会为卖方带来一定的事前收益，并为买方带来一定的事前总剩余。我们研究了当买家估值独立同分布（i.i.d.）时，所有真实机制生成的卖方-买方事前效用集合的帕累托前沿。首先，在自然的分布假设下，我们给出了帕累托前沿的完整结构刻画。例如，当估值从既正则又反MHR的分布中独立同分布抽取时，每个帕累托最优机制都是保留价不超过垄断保留价的二价拍卖。在此基础上，我们将机制选择问题解释为双边议价博弈，并分析了合作议价理论中的两个经典帕累托最优解：Kalai-Smorodinsky（KS）解与Nash解。我们证明，当估值从既正则又反MHR的分布中独立同分布抽取时，在大规模市场中两种解都能产生接近最优的福利。相反，在最坏情况MHR分布下，它们的性能表现截然不同：KS解能保证最优福利的二分之一，而Nash解可能仅获得任意小的比例。这些结果凸显了公平-效率权衡对分布结构的敏感性，并确认了KS解作为非对称双边市场中更具鲁棒性的公平性概念。