论文标题

二分会员稳定匹配问题:基于批准的匹配与申请人雇主关系

The Dichotomous Affiliate Stable Matching Problem: Approval-Based Matching with Applicant-Employer Relations

论文作者

Knittel, Marina, Dooley, Samuel, Dickerson, John P.

论文摘要

尽管稳定的婚姻问题及其变体模拟了广泛的匹配市场,但它们无法捕获复杂的代理关系,例如申请人和雇主在面试市场中的隶属关系。为了模拟这个问题,现有的有关与外部性匹配的文献允许代理人在基于自己的和分支机构的比赛中提供完整和总排名。这种完整的订购限制是不现实的,此外,该模型可能具有空心。为了解决这个问题,我们介绍了二分法会员稳定的匹配(DASM)问题,在该问题中,代理商的偏好表明对自己和他们的分支机构在市场中对其他代理商的二分法接受或拒绝。 我们还假设代理在整个比赛中的喜好取决于其(及其分支机构)匹配的一般加权估值功能。我们的结果是三重:(1)我们使用人类研究表明现实世界中的匹配排名遵循我们假定的估值函数; (2)我们通过提供一种找到这种解决方案的有效,易于实现的算法来证明始终存在稳定的解决方案。 (3)我们通过实验验证算法的效率与基于线性编程的方法的效率。

While the stable marriage problem and its variants model a vast range of matching markets, they fail to capture complex agent relationships, such as the affiliation of applicants and employers in an interview marketplace. To model this problem, the existing literature on matching with externalities permits agents to provide complete and total rankings over matchings based off of both their own and their affiliates' matches. This complete ordering restriction is unrealistic, and further the model may have an empty core. To address this, we introduce the Dichotomous Affiliate Stable Matching (DASM) Problem, where agents' preferences indicate dichotomous acceptance or rejection of another agent in the marketplace, both for themselves and their affiliates. We also assume the agent's preferences over entire matchings are determined by a general weighted valuation function of their (and their affiliates') matches. Our results are threefold: (1) we use a human study to show that real-world matching rankings follow our assumed valuation function; (2) we prove that there always exists a stable solution by providing an efficient, easily-implementable algorithm that finds such a solution; and (3) we experimentally validate the efficiency of our algorithm versus a linear-programming-based approach.

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