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

TL;DR

This paper compares uniform-price and discriminatory multi-unit auctions in repeated settings, analyzing their learning difficulty and regret bounds, revealing structural differences and conditions where uniform-price auctions enable faster learning.

Contribution

It provides a theoretical comparison of regret bounds for both auction formats, highlighting conditions under which uniform-price auctions allow faster learning rates.

Findings

Regret scales as ~√T for both formats under full information.

Regret scales as ~T^{2/3} under bandit feedback for both.

Uniform-price auctions can admit faster learning rates in certain settings.

Abstract

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.