寻找所有带有赋值约束的稳定匹配

IF 1 3区经济学 Q3 ECONOMICS

Games and Economic Behavior Pub Date : 2024-09-19 DOI:10.1016/j.geb.2024.09.004

Gregory Z. Gutin , Philip R. Neary , Anders Yeo

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引用次数: 0

摘要

在本文中，我们考虑的是受赋值约束的稳定匹配。这些匹配要求包含某些分配对，坚持不包含其他一些分配对，而且重要的是，这些匹配是稳定的。我们的主要贡献是基于迭代删除无吸引力替代方案的算法（Balinski 和 Ratier，1997 年；Gutin 等人，2023 年），它能确定给定的约束列表是否以及何时与稳定性相容。只要存在满足约束条件的稳定匹配，我们的算法就会输出所有匹配（每个解决方案的多项式时间）。这就为市场设计者提供了：(i) 测试受赋值约束的稳定匹配可行性的工具；(ii) 在可行时实施稳定匹配的工具。

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Finding all stable matchings with assignment constraints

In this paper we consider stable matchings subject to assignment constraints. These are matchings that require certain assigned pairs to be included, insist that some other assigned pairs are not, and, importantly, are stable. Our main contribution is an algorithm, based on the iterated deletion of unattractive alternatives (Balinski and Ratier, 1997; Gutin et al., 2023), that determines if and when a given list of constraints is compatible with stability. Whenever there is a stable matching that satisfies the constraints, our algorithm outputs all of them (each in polynomial time per solution). This provides market designers with (i) a tool to test the feasibility of stable matchings subject to assignment constraints, and (ii) a tool to implement them when feasible.

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来源期刊

Games and Economic Behavior ECONOMICS-

CiteScore

1.90

自引率

9.10%

发文量

148

期刊介绍： Games and Economic Behavior facilitates cross-fertilization between theories and applications of game theoretic reasoning. It consistently attracts the best quality and most creative papers in interdisciplinary studies within the social, biological, and mathematical sciences. Most readers recognize it as the leading journal in game theory. Research Areas Include: • Game theory • Economics • Political science • Biology • Computer science • Mathematics • Psychology