多单位VCG拍卖中近似保留价的克服贪婪问题
Beating Greedy For Approximating Reserve Prices in Multi-Unit VCG Auctions
摘要：
本文研究了在相关购买者参与的多单位渴望VCG拍卖中，为单位需求购买者寻找个性化保留价的问题。这个问题的输入是一组拍卖中$n$买家提交的出价的数据集。目标是找到一个保留价向量，每个买家一个，最大化所有拍卖的总收入。Roughgarden和Wang（2016）证明了这个问题是APX困难的，但允许贪婪的$\frac{1}{2}$ -近似算法。后来，Derakhshan，Golrezai和Paes Leme（2019）给出了一个基于LP的算法，实现了一个$0.68$ -近似的（重要的）特殊情况下的问题与一个单一的项目，从而击败贪婪。我们表明，在本文中，Derakhshan等人的算法。实际上并不击败贪婪的一般多项问题。这就提出了一个问题，即一般问题是否允许一个比$\frac{1}{2}$更好的近似。在本文中，我们肯定地回答这个问题，并提供了一个多项式时间算法与一个显着更好的近似因子$0.63$。我们的解决方案是基于一个新的线性规划制定，我们提出了两种不同的舍入方案。我们证明了这两个最好的和无储备的情况下（全零向量）是一个$0.63$近似。
英文摘要：
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 $n$ 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 $\frac{1}{2}$-approximation algorithm. Later, Derakhshan, Golrezai, and Paes Leme (2019) gave an LP-based algorithm achieving a $0.68$-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 better-than-$\frac{1}{2}$ approximation. In this paper, we answer this question in the affirmative and provide a polynomial-time algorithm with a significantly better approximation-factor of $0.63$. Our solution is based on a novel linear programming formulation, for which we propose two different rounding schemes. We prove that the best of these two and the no-reserve case (all-zero vector) is a $0.63$-approximation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
