Implementable stable solutions to pure matching problems

Koichi Tadenuma*, Manabu Toda

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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
Issue number2
Publication statusPublished - 1998 Mar 2
Externally publishedYes


  • 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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