Implementable stable solutions to pure matching problems

Koichi Tadenuma; Manabu Toda

doi:10.1016/S0165-4896(97)00037-1

Implementable stable solutions to pure matching problems

Koichi Tadenuma^*, Manabu Toda

^*Corresponding author for this work

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

12 Citations (Scopus)

Abstract

We consider "pure" matching problems, where being unmatched ("being single") is not a feasible choice or it is always the last choice for every agent. We show that there exists a proper subsolution of the stable solution that is implementable in Nash equilibria. Moreover, if the number of men M and the number of women W are less than or equal to 2, then any subsolution of the stable solution is implementable. However, if M=W≥3, there exists no implementable single-valued subsolution of the stable solution. All these results should be contrasted with the results in the recent literature on the matching problems with a single status.

Original language	English
Pages (from-to)	121-132
Number of pages	12
Journal	Mathematical social sciences
Volume	35
Issue number	2
DOIs	https://doi.org/10.1016/S0165-4896(97)00037-1
Publication status	Published - 1998 Mar 2
Externally published	Yes

Keywords

Implementation
Maskin monotonicity
Matching problems
Stability

ASJC Scopus subject areas

Sociology and Political Science
Social Sciences(all)
Psychology(all)
Statistics, Probability and Uncertainty

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10.1016/S0165-4896(97)00037-1

Cite this

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abstract = "We consider {"}pure{"} matching problems, where being unmatched ({"}being single{"}) is not a feasible choice or it is always the last choice for every agent. We show that there exists a proper subsolution of the stable solution that is implementable in Nash equilibria. Moreover, if the number of men M and the number of women W are less than or equal to 2, then any subsolution of the stable solution is implementable. However, if M=W≥3, there exists no implementable single-valued subsolution of the stable solution. All these results should be contrasted with the results in the recent literature on the matching problems with a single status.",

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AU - Tadenuma, Koichi

AU - Toda, Manabu

PY - 1998/3/2

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N2 - We consider "pure" matching problems, where being unmatched ("being single") is not a feasible choice or it is always the last choice for every agent. We show that there exists a proper subsolution of the stable solution that is implementable in Nash equilibria. Moreover, if the number of men M and the number of women W are less than or equal to 2, then any subsolution of the stable solution is implementable. However, if M=W≥3, there exists no implementable single-valued subsolution of the stable solution. All these results should be contrasted with the results in the recent literature on the matching problems with a single status.

AB - We consider "pure" matching problems, where being unmatched ("being single") is not a feasible choice or it is always the last choice for every agent. We show that there exists a proper subsolution of the stable solution that is implementable in Nash equilibria. Moreover, if the number of men M and the number of women W are less than or equal to 2, then any subsolution of the stable solution is implementable. However, if M=W≥3, there exists no implementable single-valued subsolution of the stable solution. All these results should be contrasted with the results in the recent literature on the matching problems with a single status.

KW - Implementation

KW - Maskin monotonicity

KW - Matching problems

KW - Stability

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VL - 35

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JO - Mathematical social sciences

JF - Mathematical social sciences

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ER -

Implementable stable solutions to pure matching problems

Abstract

Keywords

ASJC Scopus subject areas

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