Implementable stable solutions to pure matching problems

Koichi Tadenuma, Manabu Toda

Research output: Contribution to journalArticle

11 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 languageEnglish
Pages (from-to)121-132
Number of pages12
JournalMathematical Social Sciences
Volume35
Issue number2
Publication statusPublished - 1998 Mar 2
Externally publishedYes

Fingerprint

Subsolution
Stable Solution
Matching Problem
Single valued
Less than or equal to
Nash Equilibrium
Matching problem
Nash equilibrium
literature

Keywords

  • Implementation
  • Maskin monotonicity
  • Matching problems
  • Stability

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Economics and Econometrics

Cite this

Implementable stable solutions to pure matching problems. / Tadenuma, Koichi; Toda, Manabu.

In: Mathematical Social Sciences, Vol. 35, No. 2, 02.03.1998, p. 121-132.

Research output: Contribution to journalArticle

@article{7c0d27095d6d4c6c8b2dca3a042483e4,
title = "Implementable stable solutions to pure matching problems",
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.",
keywords = "Implementation, Maskin monotonicity, Matching problems, Stability",
author = "Koichi Tadenuma and Manabu Toda",
year = "1998",
month = "3",
day = "2",
language = "English",
volume = "35",
pages = "121--132",
journal = "Mathematical Social Sciences",
issn = "0165-4896",
publisher = "Elsevier",
number = "2",

}

TY - JOUR

T1 - Implementable stable solutions to pure matching problems

AU - Tadenuma, Koichi

AU - Toda, Manabu

PY - 1998/3/2

Y1 - 1998/3/2

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

UR - http://www.scopus.com/inward/record.url?scp=0001461754&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001461754&partnerID=8YFLogxK

M3 - Article

VL - 35

SP - 121

EP - 132

JO - Mathematical Social Sciences

JF - Mathematical Social Sciences

SN - 0165-4896

IS - 2

ER -