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/√k) approximation to the optimal mechanism; the worst-case ratio is maximized at about 2.47 when k=1and converges to 2 as k grows. This indicates that the gains from third-degree price discrimination are mild in large markets.

Yaonan Jin is an Assistant Professor in the Department of Computer Science and Engineering at the Hong Kong University of Science and Technology. Before joining HKUST, he conducted theoretical computer science research at Huawei’s Taylor Lab, working with Pinyan Lu. He obtained his PhD from Columbia University in 2023 (advised by Xi Chen and Rocco Servedio). Prior to that, he obtained his MPhil from Hong Kong University of Science and Technology (advised by Qi Qi) and his BEng from Shanghai Jiao Tong University.