Monotonicity and consistency in matching markets

Manabu Toda*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


Objective: To obtain axiomatic characterizations of the core of one-to-one and one-to-many matching markets. Methods: The axioms recently applied to characterize the core of assignment games were adapted to the models of this paper. Results: The core of one-to-one matching markets is characterized by two different lists of axioms. The first one consists of weak unanimity, population monotonicity, and Maskin monotonicity. The second consists of weak unanimity, population monotonicity, and consistency. If we allow for weak preferences, the core is characterized by weak unanimity, population monotonicity, Maskin monotonicity, and consistency. For one-to-many matchings, the same lists as for the case of strict preferences characterize the core. Conclusions: The cores of the discrete matching markets are characterized by axioms that almost overlap with the axioms characterizing the core of the continuous matching markets. This provides an axiomatic explanation for the observations in the literature that almost parallel properties are obtained for the core of the two models. We observe that Maskin monotonicity is closely related to consistency in matching markets.

Original languageEnglish
Pages (from-to)13-31
Number of pages19
JournalInternational Journal of Game Theory
Issue number1
Publication statusPublished - 2006 Apr 1


  • Consistency
  • Maskin monotonicity
  • Population monotonicity
  • Two-sided matchings

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (miscellaneous)
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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