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Comparing Uniform Price and Discriminatory Multi-Unit Auc...
Marius Potfer, Vianney Perchet · 2025-10-22 · via stat.ML updates on arXiv.org

Repeated multi-unit auctions, where a seller allocates multiple identical items over many rounds, are common mechanisms in electricity markets and treasury auctions. We compare the two predominant formats: uniform-price and discriminatory auctions, focusing on the perspective of a single bidder learning to bid against stochastic adversaries. We characterize the learning difficulty in each format, showing that the regret scales similarly for both auction formats under both full-information and bandit feedback, as $\tildeΘ ( \sqrt{T} )$ and $\tildeΘ ( T^{2/3} )$, respectively. However, analysis beyond worst-case regret reveals structural differences: uniform-price auctions may admit faster learning rates, with regret scaling as $\tildeΘ ( \sqrt{T} )$ in settings where discriminatory auctions remain at $\tildeΘ ( T^{2/3} )$. Finally, we provide a specific analysis for auctions in which the other participants are symmetric and have unit-demand, and show that in these instances, a similar regret rate separation appears.