Linear Program-Based Approximation for Personalized Reserve Prices
Name
1905.01526.pdf
Description
Accepted version
Size
573.87 KB
Format
Adobe PDF
Checksum (MD5)
6753dc1fe59fef05e0b2931218390055
Author(s)
Derakhshan, Mahsa
Golrezaei, Negin
Paes Leme, Renato
Date Issued
2022
Journal
Management Science
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Citation
Derakhshan, Mahsa, Golrezaei, Negin and Paes Leme, Renato. 2022. "Linear Program-Based Approximation for Personalized Reserve Prices." Management Science, 68 (3).
Version
Author's final manuscript
Abstract
We study the problem of computing data-driven personalized reserve prices in eager second price auctions without having any assumption on valuation distributions. Here, the input is a data set that contains the submitted bids of n buyers in a set of auctions, and the problem is to return personalized reserve prices r that maximize the revenue earned on these auctions by running eager second price auctions with reserve r. For this problem, which is known to be NP complete, we present a novel linear program (LP) formulation and a rounding procedure, which achieves a 0.684 approximation. This improves over the [Formula: see text]-approximation algorithm from Roughgarden and Wang. We show that our analysis is tight for this rounding procedure. We also bound the integrality gap of the LP, which shows that it is impossible to design an algorithm that yields an approximation factor larger than 0.828 with respect to this LP. This paper was accepted by Chung Piaw Teo, Management Science Special Section on Data-Driven Prescriptive Analytics.
MIT Department
Sloan School of Management
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1287/MNSC.2020.3897
