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A theory of stability in many-to-many matching markets

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Author Info

  • Echenique, Federico

    ()
    (California Institute of Technology)

  • Oviedo, Jorge

    ()
    (Universidad Nacional de San Luis, Argentina)

Abstract

We develop a theory of stability in many-to-many matching markets. We give conditions under which the setwise-stable set, a core-like concept, is nonempty and can be approached through an algorithm. The usual core may be empty. The setwise-stable set coincides with the pairwise-stable set and with the predictions of a non-cooperative bargaining model. The setwise-stable set possesses the conflict/coincidence of interest properties from many-to-one, and one-to-one models. The theory parallels the standard theory of stability for many-to-one, and one-to-one, models. We provide results for a number of core-like solutions, besides the setwise-stable set.

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Bibliographic Info

Article provided by Econometric Society in its journal Theoretical Economics.

Volume (Year): 1 (2006)
Issue (Month): 2 (June)
Pages: 233-273

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Handle: RePEc:the:publsh:139

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Web page: http://econtheory.org

Related research

Keywords: Two-sided matching; cooperative game theory; core;

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References

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  1. 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).
  2. Federico Echenique & Jorge Oviedo, 2003. "Core Many-to-one Matchings by Fixed-point Methods," Game Theory and Information 0302001, EconWPA.
  3. José Alcalde Pérez & Antonio Romero-Medina & David Pérez-Castrillo, 1997. "Hiring procedures to implement stable allocations," Working Papers. Serie AD 1997-10, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  4. Klijn, F. & Masso, J., 1999. "Weak Stability and a Bargaining Set for the Marriage Model," Discussion Paper 1999-114, Tilburg University, Center for Economic Research.
  5. Elliott Peranson & Alvin E. Roth, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," American Economic Review, American Economic Association, vol. 89(4), pages 748-780, September.
  6. Sonmez, T., 1995. "Strategy-Proofness in Many-To-One Matching Problems," Papers 95-01, Michigan - Center for Research on Economic & Social Theory.
  7. Zhou Lin, 1994. "A New Bargaining Set of an N-Person Game and Endogenous Coalition Formation," Games and Economic Behavior, Elsevier, vol. 6(3), pages 512-526, May.
  8. Salvador Barbera & Hugo Sonnenschein & Lin Zhou, 1990. "Voting by Committees," Cowles Foundation Discussion Papers 941, Cowles Foundation for Research in Economics, Yale University.
  9. Dutta, Bhaskar & Masso, Jordi, 1997. "Stability of Matchings When Individuals Have Preferences over Colleagues," Journal of Economic Theory, Elsevier, vol. 75(2), pages 464-475, August.
  10. Roth, Alvin E. & Sotomayor, Marilda, 1988. "Interior points in the core of two-sided matching markets," Journal of Economic Theory, Elsevier, vol. 45(1), pages 85-101, June.
  11. Paul Milgrom, 2003. "Matching with Contracts," Working Papers 03003, Stanford University, Department of Economics.
  12. Alcalde, Jose & Romero-Medina, Antonio, 2000. "Simple Mechanisms to Implement the Core of College Admissions Problems," Games and Economic Behavior, Elsevier, vol. 31(2), pages 294-302, May.
  13. Hideo Konishi & M. Utku Ünver, 2003. "Credible Group Stability in Multi-Partner Matching Problems," Working Papers 2003.115, Fondazione Eni Enrico Mattei.
  14. 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.
  15. Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 55-70, July.
  16. Adachi, Hiroyuki, 2000. "On a characterization of stable matchings," Economics Letters, Elsevier, vol. 68(1), pages 43-49, July.
  17. 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.
  18. 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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