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 full-information and bandit feedback, as $\tilde{\Theta }(\sqrt{T})$ and $\tilde{\Theta }(T^{2/3})$, respectively. However, analysis beyond worst-case regret reveals structural differences: uniform-price auctions may admit faster learning rates, with regret scaling as $\tilde{\Theta }(\sqrt{T})$ in settings where discriminatory auctions remain at $\tilde{\Theta }(T^{2/3})$.

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.