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

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  • ,

    (California Institute of Technology)

  • ,

    (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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  • , & ,, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, vol. 1(2), pages 233-273, June.
    • Handle: RePEc:the:publsh:139
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    1. 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.
    2. Klijn, Flip & Masso, Jordi, 2003. "Weak stability and a bargaining set for the marriage model," Games and Economic Behavior, Elsevier, vol. 42(1), pages 91-100, January.
    3. Ahmet Alkan, 2001. "original papers : On preferences over subsets and the lattice structure of stable matchings," Review of Economic Design, Springer;Society for Economic Design, vol. 6(1), pages 99-111.
    4. Charles Blair, 1988. "The Lattice Structure of the Set of Stable Matchings with Multiple Partners," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 619-628, November.
    5. 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.
    6. Echenique, Federico & Oviedo, Jorge, 2004. "Core many-to-one matchings by fixed-point methods," Journal of Economic Theory, Elsevier, vol. 115(2), pages 358-376, April.
    7. Hideo Konishi & M. Utku Ünver, 2003. "Credible Group Stability in Multi-Partner Matching Problems," Working Papers 2003.115, Fondazione Eni Enrico Mattei.
    8. Alcalde, Jose & Perez-Castrillo, David & Romero-Medina, Antonio, 1998. "Hiring Procedures to Implement Stable Allocations," Journal of Economic Theory, Elsevier, vol. 82(2), pages 469-480, October.
    9. Adachi, Hiroyuki, 2000. "On a characterization of stable matchings," Economics Letters, Elsevier, vol. 68(1), pages 43-49, July.
    10. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    11. 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.
    12. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    13. Tamás Fleiner, 2003. "A Fixed-Point Approach to Stable Matchings and Some Applications," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 103-126, February.
    14. Tayfun Sönmez, 1994. "Strategy-proofness in many-to-one matching problems," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 365-380, December.
    15. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    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. 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.
    18. 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.
    19. 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.
    20. 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.
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    More about this item

    Keywords

    Two-sided matching; cooperative game theory; core;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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