Unique stable matchings

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

doi:10.1016/j.geb.2023.07.010

Unique stable matchings

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

Mathematics and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	529-547
Number of pages	19
Journal	Games and Economic Behavior
Volume	141
DOIs	https://doi.org/10.1016/j.geb.2023.07.010
Publication status	Published - Sept 2023

Keywords

Acyclic preferences
Iterated deletion of unattractive alternatives
Normal-form
Unique stable matching

ASJC Scopus subject areas

Finance
Economics and Econometrics

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10.1016/j.geb.2023.07.010

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title = "Unique stable matchings",

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.",

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T1 - Unique stable matchings

AU - Gutin, Gregory Z.

AU - Neary, Philip R.

AU - Yeo, Anders

PY - 2023/9

Y1 - 2023/9

N2 - 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.

AB - 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.

KW - Acyclic preferences

KW - Iterated deletion of unattractive alternatives

KW - Normal-form

KW - Unique stable matching

UR - https://www.scopus.com/pages/publications/85167808937

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DO - 10.1016/j.geb.2023.07.010

M3 - Article

AN - SCOPUS:85167808937

SN - 0899-8256

VL - 141

SP - 529

EP - 547

JO - Games and Economic Behavior

JF - Games and Economic Behavior

ER -

Unique stable matchings

Abstract

Keywords

ASJC Scopus subject areas

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