Comparing Uniform Price and Discriminatory Multi-Unit Auctions through Regret Minimization

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 fullinformation and bandit feedback, as Θ( T)and Θ(T2/3), respectively. However, analysis beyond worst-case regret reveals structural differences: uniform-price auctions may admit faster learning rates, with regret scaling as Θ( T)in settings where discriminatory auctions remain at Θ(T2/3). Finally, we provide a specific analysis for auctions in which the other participants are symmetric and have unitdemand, and show that in these instances, a similar regret rate separation appears.