### 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 |

Publication status | Published - 1998 Mar 2 |

Externally published | Yes |

### Fingerprint

### Keywords

- Implementation
- Maskin monotonicity
- Matching problems
- Stability

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Economics and Econometrics

### Cite this

*Mathematical Social Sciences*,

*35*(2), 121-132.

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

Research output: Contribution to journal › Article

*Mathematical Social Sciences*, vol. 35, no. 2, pp. 121-132.

}

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

AN - SCOPUS:0001461754

VL - 35

SP - 121

EP - 132

JO - Mathematical Social Sciences

JF - Mathematical Social Sciences

SN - 0165-4896

IS - 2

ER -