Posted price mechanisms are prevalent in allocating goods within online marketplaces due to their simplicity and practical efficiency. We explore a fundamental scenario where buyers' valuations are independent and identically distributed, focusing specifically on the allocation of a single unit. Inspired by the rapid growth and scalability of modern online marketplaces, we investigate optimal performance guarantees under the assumption of a significantly large market. We show a large market benefit when using fixed prices, improving the known guarantee of $1-1/e\approx 0.632$ to $0.712$. We then study the case of selling $k$ identical units, and we prove that the optimal fixed price guarantee approaches $1-1/\sqrt{2k \pi}$, which implies that the large market advantage vanishes as $k$ grows. We use real-world auction data to test our fixed price policies in the large market regime. Next, under the large market assumption, we show that the competition complexity for the optimal posted price mechanism is constant, and we identify precise scaling factors for the number of bidders that enable it to match benchmark performance. Remarkably, our findings break previously established worst-case impossibility results, underscoring the practical robustness and efficiency of posted pricing in large-scale marketplaces.

翻译：挂牌定价机制因其简洁性和实际效率，在在线市场商品分配中广泛应用。本文探讨买家估值独立同分布的基本场景，特别聚焦于单一单位的分配问题。受现代在线市场快速增长与可扩展性的启发，我们在市场规模显著扩大的假设下研究最优性能保证。我们证明了采用固定价格时存在大市场效益，将已知保证$1-1/e\approx 0.632$提升至$0.712$。随后我们研究销售$k$个相同单位的情况，证明最优固定价格保证趋近于$1-1/\sqrt{2k \pi}$，这意味着大市场优势随$k$增大而消失。我们使用真实拍卖数据测试大市场体系下的固定价格策略。进一步地，在大市场假设下，我们证明最优挂牌定价机制的竞争复杂度为常数，并确定了使其达到基准性能所需的投标人数量的精确比例因子。值得注意的是，我们的研究突破了先前建立的最坏情况不可能性结果，凸显了挂牌定价在大规模市场中的实际鲁棒性与效率。