Unique stable matchings

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

*Kontaktforfatter

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Abstract

In this paper we consider the issue of a unique prediction in one-to-one two-sided matching markets, as defined by Gale and Shapley (1962), and we prove the following: Theorem Let P be a one-to-one two-sided matching market and let P be its associated normal form, a (weakly) smaller matching market with the same set of stable matchings that can be obtained using procedures introduced in Irving and Leather (1986) and Balinski and Ratier (1997). The following three statements are equivalent: (a) P has a unique stable matching. (b) Preferences on P are acyclic, as defined by Chung (2000). (c) In P every market participant's preference list is a singleton.

OriginalsprogEngelsk
TidsskriftGames and Economic Behavior
Vol/bind141
Sider (fra-til)529-547
Antal sider19
ISSN0899-8256
DOI
StatusUdgivet - sep. 2023

Bibliografisk note

Funding Information:
We are grateful to Jesper Bagger, Claudia Cerrone, Dongkyu Chang, Vince Crawford, Julie Cullen, Audrey Hu, Sung-Ha Hwang, Miguel Meléndez-Jiménez, Kohei Kawaguchi, Christian Keeling, Onur Kesten, Chulyoung Kim, Bettina Klaus, Yunan Li, Wooyoung Lim, Jordi Massó, Frances P. Ruane, Joel Sobel, Rui Tang, Alex Teytelboym, Alexander Vickery, Joel Watson, Qinggong Wu, Wenji Xu, and participants in seminar presentations at City University of Hong Kong, Hong Kong University of Science and Technology, Korea Advanced Institute of Science and Technology, Universidad de Málaga, and Yonsei University for helpful comments. Two anonymous referees and an associate editor made many excellent suggestions that improved the paper considerably. Any remaining errors are ours. Anders Yeo's research was supported by the Danish Council for Independent Research under grant number DFF 7014-00037B.

Funding Information:
We are grateful to Jesper Bagger, Claudia Cerrone, Dongkyu Chang, Vince Crawford, Julie Cullen, Audrey Hu, Sung-Ha Hwang, Miguel Meléndez-Jiménez, Kohei Kawaguchi, Christian Keeling, Onur Kesten, Chulyoung Kim, Bettina Klaus, Yunan Li, Wooyoung Lim, Jordi Massó, Frances P. Ruane, Joel Sobel, Rui Tang, Alex Teytelboym, Alexander Vickery, Joel Watson, Qinggong Wu, Wenji Xu, and participants in seminar presentations at City University of Hong Kong, Hong Kong University of Science and Technology, Korea Advanced Institute of Science and Technology, Universidad de Málaga, and Yonsei University for helpful comments. Two anonymous referees and an associate editor made many excellent suggestions that improved the paper considerably. Any remaining errors are ours. Anders Yeo's research was supported by the Danish Council for Independent Research under grant number DFF 7014-00037B .

Publisher Copyright:
© 2023 The Author(s)

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