A flow-based ascending auction to compute buyer-optimal Walrasian prices

IF 1.6 4区计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE Networks Pub Date : 2024-04-16 DOI:10.1002/net.22218

Katharina Eickhoff, S. Thomas McCormick, Britta Peis, Niklas Rieken, Laura Vargas Koch

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Abstract

We consider a market where a set of objects is sold to a set of buyers, each equipped with a valuation function for the objects. The goal of the auctioneer is to determine reasonable prices together with a stable allocation. One definition of “reasonable” and “stable” is a Walrasian equilibrium, which is a tuple consisting of a price vector together with an allocation satisfying the following desirable properties: (i) the allocation is market-clearing in the sense that as much as possible is sold, and (ii) the allocation is stable in the sense that every buyer ends up with an optimal set with respect to the given prices. Moreover, “buyer-optimal” means that the prices are smallest possible among all Walrasian prices. In this paper, we present a combinatorial network flow algorithm to compute buyer-optimal Walrasian prices in a multi-unit matching market with truncated additive valuation functions. The algorithm can be seen as a generalization of the classical housing market auction and mimics the very natural procedure of an ascending auction. We use our structural insights to prove monotonicity of the buyer-optimal Walrasian prices with respect to changes in supply or demand.

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计算买方最优 Walrasian 价格的基于流量的升序拍卖

我们考虑这样一个市场：一组物品出售给一组买家，每个买家都对物品有一个估值函数。拍卖人的目标是确定合理的价格和稳定的分配。合理 "和 "稳定 "的定义之一是瓦尔拉斯均衡，它是由价格向量和满足以下理想属性的分配组成的元组：(i) 分配是市场清算的，即尽可能多的物品被售出；(ii) 分配是稳定的，即每个买方最终都能获得一组与给定价格相关的最优物品。此外，"买方最优 "意味着价格是所有瓦尔拉斯价格中最小的。在本文中，我们提出了一种组合网络流算法，用于计算具有截断加值函数的多单位匹配市场中的买方最优 Walrasian 价格。该算法可视为经典住房市场拍卖的一般化，并模仿了非常自然的升序拍卖程序。我们利用结构洞察力证明了买方最优 Walrasian 价格在供应或需求变化方面的单调性。

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来源期刊

Networks 工程技术-计算机：硬件

CiteScore

4.40

自引率

9.50%

发文量

审稿时长

12 months

期刊介绍： Network problems are pervasive in our modern technological society, as witnessed by our reliance on physical networks that provide power, communication, and transportation. As well, a number of processes can be modeled using logical networks, as in the scheduling of interdependent tasks, the dating of archaeological artifacts, or the compilation of subroutines comprising a large computer program. Networks provide a common framework for posing and studying problems that often have wider applicability than their originating context. The goal of this journal is to provide a central forum for the distribution of timely information about network problems, their design and mathematical analysis, as well as efficient algorithms for carrying out optimization on networks. The nonstandard modeling of diverse processes using networks and network concepts is also of interest. Consequently, the disciplines that are useful in studying networks are varied, including applied mathematics, operations research, computer science, discrete mathematics, and economics. Networks publishes material on the analytic modeling of problems using networks, the mathematical analysis of network problems, the design of computationally eﬃcient network algorithms, and innovative case studies of successful network applications. We do not typically publish works that fall in the realm of pure graph theory (without signiﬁcant algorithmic and modeling contributions) or papers that deal with engineering aspects of network design. Since the audience for this journal is then necessarily broad, articles that impact multiple application areas or that creatively use new or existing methodologies are especially appropriate. We seek to publish original, well-written research papers that make a substantive contribution to the knowledge base. In addition, tutorial and survey articles are welcomed. All manuscripts are carefully refereed.