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A Theory of Stability in Many-to-many Matching Markets

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Author Info

  • Federico Echenique

    (Caltech)

  • Jorge Oviedo

    (Universidad Nacional de San Luis)

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 set-wise stable set possesses the canonical 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

Paper provided by EconWPA in its series Game Theory and Information with number 0401002.

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Length: 45 pages
Date of creation: 18 Jan 2004
Date of revision:
Handle: RePEc:wpa:wuwpga:0401002

Note: Type of Document - pdf; prepared on linux; to print on postscript; pages: 45
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Web page: http://128.118.178.162

Related research

Keywords: many-to-many matchings; substitutability; tarski fixed point theorem; setwise stability; core;

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References

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  1. Salvador Barbera & Hugo Sonnenschein & Lin Zhou, 1990. "Voting by Committees," Cowles Foundation Discussion Papers 941, Cowles Foundation for Research in Economics, Yale University.
  2. Hideo Konishi & Utku Unver, 2004. "Credible Group Stability in Multi-Partner Matching Problems," Econometric Society 2004 North American Summer Meetings 32, Econometric Society.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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).
  8. 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).
  9. Adachi, Hiroyuki, 2000. "On a characterization of stable matchings," Economics Letters, Elsevier, vol. 68(1), pages 43-49, July.
  10. Federico Echenique & Jorge Oviedo, 2003. "Core Many-to-one Matchings by Fixed-point Methods," Game Theory and Information 0302001, EconWPA.
  11. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
  12. Tayfun Sönmez, 1994. "Strategy-proofness in many-to-one matching problems," Review of Economic Design, Springer, vol. 1(1), pages 365-380, December.
  13. 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.
  14. José Alcalde Pérez & Antonio Romero-Medina, 1996. "Simple mechanisms to implement the core of college admissions problems," Working Papers. Serie AD 1996-13, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  15. 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.
  16. Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 55-70, July.
  17. 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.
  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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