Departmental Bulletin Paper Random paths to stability in Danilov’s three-sided matching model

Yusuke, Samejima

43 ( 2 )  , pp.101 - 114 , 2018-03 , 東洋大学経済研究会
ISSN:0385-0358
NCID:AN00071538
Description
We investigate three-sided matching problems where three kinds of agents, men, women, and cats are matched. Without any restrictions on preferences of agents, a stable matching does not necessarily exist for a three-sided matching problem. However, Danilov [2003] has proved the existence of a stable matching for any three-sided matching problem if preference domains for men and women are restricted in a certain way. In the present paper, we show that, starting from an arbitrary unstable matching, there exists a finite sequence of successive blockings leading to some stable matching for a three-sided matching problem in Danilov’s model, as Roth and Vande Vate [1990] have proved for two-sided matching problems. The result implies that a decentralized process of successive blockings by randomly chosen blocking agents will converge to a stable matching.
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