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

  • Martínez, Ruth
  • Massó, Jordi
  • Neme, Alejandro
  • Oviedo, Jorge

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.

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Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 46 (2010)
Issue (Month): 5 (September)
Pages: 937-949

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Handle: RePEc:eee:mateco:v:46:y:2010:i:5:p:937-949
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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  1. Dutta, B. & Masso, J., 1996. "Stability of Matchings when Individuals Have Preferences Over Colleagues," UFAE and IAE Working Papers 325.96, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
  3. Ahmet Alkan, 2001. "original papers : On preferences over subsets and the lattice structure of stable matchings," Review of Economic Design, Springer, vol. 6(1), pages 99-111.
  4. Tayfun Sönmez, 1994. "Strategy-proofness in many-to-one matching problems," Review of Economic Design, Springer, vol. 1(1), pages 365-380, December.
  5. Roth, Alvin E & Xing, Xiaolin, 1994. "Jumping the Gun: Imperfections and Institutions Related to the Timing of Market Transactions," American Economic Review, American Economic Association, vol. 84(4), pages 992-1044, September.
  6. Barbera, S. & Sonnenschein, H., 1988. "Voting By Quota And Committee," UFAE and IAE Working Papers 95-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  7. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
  8. Lars Ehlers & Bettina Klaus, 2003. "Coalitional strategy-proof and resource-monotonic solutions for multiple assignment problems," Social Choice and Welfare, Springer, vol. 21(2), pages 265-280, October.
  9. Ruth Mart?ez & Jordi MassóAuthor-Email: jordi.masso@uab.es & Alejandro Neme & Jorge Oviedo, 2003. "On group strategy-proof mechanisms for a many-to-one matching model," UFAE and IAE Working Papers 577.03, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  10. Salvador Barbera & Hugo Sonnenschein & Lin Zhou, 1990. "Voting by Committees," Cowles Foundation Discussion Papers 941, Cowles Foundation for Research in Economics, Yale University.
  11. Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2000. "Single Agents and the Set of Many-to-One Stable Matchings," Journal of Economic Theory, Elsevier, vol. 91(1), pages 91-105, March.
  12. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
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