We study revenue maximization when a seller offers $k$ identical units to ex ante heterogeneous, unit-demand buyers. While anonymous pricing can be $Θ(\log k)$ worse than optimal in general multi-unit environments, we show that this pessimism disappears in large markets, where no single buyer accounts for a non-negligible share of optimal revenue. Under (quasi-)regularity, anonymous pricing achieves a $2+O(1/\sqrt{k})$ approximation to the optimal mechanism; the worst-case ratio is maximized at about $2.47$ when $k=1$ and converges to $2$ as $k$ grows. This indicates that the gains from third-degree price discrimination are mild in large markets.

翻译：本文研究卖方将$k$个同质商品出售给事前异质性单位需求买家时的收益最大化问题。虽然在一般多单位销售环境中，匿名定价可能比最优机制差$Θ(\log k)$倍，但我们证明这种悲观结论在大规模市场中并不成立——在此类市场中，任何单一买家对最优收益的贡献均不可忽略。在（拟）正则性条件下，匿名定价可实现$2+O(1/\sqrt{k})$倍于最优机制的近似比；最坏情况比率在$k=1$时达到最大值约$2.47$，并随着$k$增大收敛至$2$。这表明在大规模市场中，三级价格歧视带来的收益提升是有限的。