The Query Complexity of Uniform Pricing
Houshuang Chen, Yaonan Jin, Pinyan Lu, Chihao Zhang

TL;DR
This paper investigates the query complexity of uniform pricing in multi-distribution settings, establishing lower bounds that match known upper bounds and highlighting the limitations of distribution regularity conditions in reducing complexity.
Contribution
It proves near-matching lower bounds for query complexity and regret minimization in multi-distribution uniform pricing, extending prior single-distribution results.
Findings
Lower bound of (^{-3}) for two regular or three MHR distributions.
Lower bound of (T^{2/3}) for regret minimization in multi-distribution cases.
Contrast with single-distribution case where bounds are tighter.
Abstract
Real-world pricing mechanisms are typically optimized using training data, a setting corresponding to the \textit{pricing query complexity} problem in Mechanism Design. The previous work [LSTW23] studies the \textit{single-distribution} case, with tight bounds of for a \textit{general} distribution and for either a \textit{regular} or \textit{monotone-hazard-rate (MHR)} distribution, where denotes the (additive) revenue loss of a learned uniform price relative to the Bayesian-optimal uniform price. This can be directly interpreted as ``the query complexity of the {\em \textsf{Uniform Pricing}} mechanism, in the \textit{single-distribution} case''. Yet in the \textit{multi-distribution} case, can the regularity and MHR conditions still lead to improvements over the tight bound…
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Taxonomy
TopicsAuction Theory and Applications · Game Theory and Applications · Consumer Market Behavior and Pricing
