The Blocking Lemma for a many-to-one matching model

Ruth Martínez, Jordi Massó, Alejandro Neme, Jorge Oviedo

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)

Abstract

The Blocking Lemma identifies a particular blocking pair for each non-stable and individually rational matching that is preferred by some agents of one side of the market to their optimal stable matching. Its interest lies in the fact that it has been an instrumental result to prove key results on matching. For instance, the fact that in the college admissions problem the workers-optimal stable mechanism is group strategy-proof for the workers and the strong stability theorem in the marriage model follow directly from the Blocking Lemma. However, it is known that the Blocking Lemma and its consequences do not hold in the general many-to-one matching model in which firms have substitutable preference relations. We show that the Blocking Lemma holds for the many-to-one matching model in which firms' preference relations are, in addition to substitutable, quota q-separable. We also show that the Blocking Lemma holds on a subset of substitutable preference profiles if and only if the workers-optimal stable mechanism is group strategy-proof for the workers on this subset of profiles. © 2010.
Original languageEnglish
Pages (from-to)937-949
JournalJournal of Mathematical Economics
Volume46
DOIs
Publication statusPublished - 20 Sep 2010

Keywords

  • Blocking Lemma
  • C78
  • D71
  • D78
  • Matching
  • Stability

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