Truthful Matching with Online Items and Offline Agents

IF 0.9 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Algorithmica Pub Date : 2024-01-16 DOI:10.1007/s00453-023-01202-3

Michal Feldman, Federico Fusco, Stefano Leonardi, Simon Mauras, Rebecca Reiffenhäuser

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Abstract

We study truthful mechanisms for welfare maximization in online bipartite matching. In our (multi-parameter) setting, every buyer is associated with a (possibly private) desired set of items, and has a private value for being assigned an item in her desired set. Unlike most online matching settings, where agents arrive online, in our setting the items arrive one by one in an adversarial order while the buyers are present for the entire duration of the process. This poses a significant challenge to the design of truthful mechanisms, due to the ability of buyers to strategize over future rounds. We provide an almost full picture of the competitive ratios in different scenarios, including myopic vs. non-myopic agents, tardy vs. prompt payments, and private vs. public desired sets. Among other results, we identify the frontier up to which the celebrated \(e/(e-1)\) competitive ratio for the vertex-weighted online matching of Karp, Vazirani and Vazirani extends to truthful agents and online items.

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在线项目和离线代理的真实匹配

我们研究在线双向匹配中福利最大化的真实机制。在我们的（多参数）设置中，每个买方都与一组（可能是私人的）所需物品相关联，并且对被分配到其所需物品中的物品具有私人价值。与大多数在线匹配设置（代理在线到达）不同的是，在我们的设置中，物品按对抗顺序逐一到达，而买家在整个过程中都在场。由于买方有能力在未来几轮中制定策略，这对设计真实机制提出了巨大挑战。我们提供了不同情况下竞争比率的几乎全貌，包括近视代理与非近视代理、延迟付款与及时付款，以及私人期望集与公共期望集。在其他结果中，我们确定了卡普、瓦齐拉尼和瓦齐拉尼的顶点加权在线匹配的著名竞争比率（e/(e-1)\）扩展到真实代理和在线项目的边界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algorithmica 工程技术-计算机：软件工程

CiteScore

2.80

自引率

9.10%

发文量

158

审稿时长

12 months

期刊介绍： Algorithmica is an international journal which publishes theoretical papers on algorithms that address problems arising in practical areas, and experimental papers of general appeal for practical importance or techniques. The development of algorithms is an integral part of computer science. The increasing complexity and scope of computer applications makes the design of efficient algorithms essential. Algorithmica covers algorithms in applied areas such as: VLSI, distributed computing, parallel processing, automated design, robotics, graphics, data base design, software tools, as well as algorithms in fundamental areas such as sorting, searching, data structures, computational geometry, and linear programming. In addition, the journal features two special sections: Application Experience, presenting findings obtained from applications of theoretical results to practical situations, and Problems, offering short papers presenting problems on selected topics of computer science.