Beating Greedy For Approximating Reserve Prices in Multi-Unit VCG Auctions
Mahsa Derakhshan, David M. Pennock, Aleksandrs Slivkins

TL;DR
This paper presents a new polynomial-time algorithm that improves the approximation factor for finding personalized reserve prices in multi-unit VCG auctions with correlated buyers, surpassing previous greedy and LP-based methods.
Contribution
The paper introduces a novel LP formulation and two rounding schemes that achieve a 0.63-approximation, improving over the prior 0.5 and 0.68 approximations.
Findings
New LP-based algorithm with 0.63 approximation factor
Proves the no-reserve case is a 0.63-approximation
Demonstrates previous LP-based method does not beat greedy in general
Abstract
We study the problem of finding personalized reserve prices for unit-demand buyers in multi-unit eager VCG auctions with correlated buyers. The input to this problem is a dataset of submitted bids of buyers in a set of auctions. The goal is to find a vector of reserve prices, one for each buyer, that maximizes the total revenue across all auctions. Roughgarden and Wang (2016) showed that this problem is APX-hard but admits a greedy -approximation algorithm. Later, Derakhshan, Golrezai, and Paes Leme (2019) gave an LP-based algorithm achieving a -approximation for the (important) special case of the problem with a single-item, thereby beating greedy. We show in this paper that the algorithm of Derakhshan et al. in fact does not beat greedy for the general multi-item problem. This raises the question of whether or not the general problem admits a…
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Taxonomy
TopicsAuction Theory and Applications · Game Theory and Voting Systems · Consumer Market Behavior and Pricing
