A New Approach to the Pareto Stable Matching Problem
A New Approach to the Pareto Stable Matching Problem
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DOI：
10.1287/moor.2013.0627
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发表时间：
2012-07
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影响因子：
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通讯作者：
Naoyuki Kamiyama
中科院分区：
文献类型：
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作者：
Naoyuki Kamiyama
在双边匹配市场中，Gale和Shapley提出的稳定性概念是最重要的解概念之一。本文研究了双边无差异匹配市场中匹配的稳定性问题。在具有无差异的双边匹配市场中，稳定性并不能保证帕累托有效。Erdil和Ergin证明了在多对一无差异匹配市场中总存在一个稳定的Pareto有效匹配，并给出了一个多项式时间算法; Chen证明了在多对多无差异匹配市场中总存在一个稳定的Pareto有效匹配，并给出了一个多项式时间算法。我们提出了一种新的方法来寻找一个稳定的和帕累托有效的匹配在一个多对多的匹配市场与无差异的问题。我们的算法是一个替代的证据存在一个稳定的和帕累托有效的匹配在一个多对多匹配市场的无差异。
In two-sided matching markets, the concept of stability proposed by Gale and Shapley is one of the most important solution concepts. In this paper, we consider a problem related to stability of a matching in a two-sided matching market with indifferences. It is known that stability does not guarantee Pareto efficiency in a two-sided matching market with indifferences. However, Erdil and Ergin proved that there always exists a stable and Pareto efficient matching in a many-to-one matching market with indifferences and gave a polynomial-time algorithm for finding it. Later on, Chen proved that there always exists a stable and Pareto efficient matching in a many-to-many matching market with indifferences and gave a polynomial-time algorithm for finding it. In this paper, we propose a new approach to the problem of finding a stable and Pareto efficient matching in a many-to-many matching market with indifferences. Our algorithm is an alternative proof of the existence of a stable and Pareto efficient matching in a many-to-many matching market with indifferences.