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

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  • Federico Echenique
  • Jorge Oviedo

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 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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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 666156000000000374.

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Date of creation: 18 Nov 2003
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Handle: RePEc:cla:levarc:666156000000000374

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  1. 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.
  2. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, Econometric Society, vol. 52(1), pages 47-57, January.
  3. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, Econometric Society, vol. 59(3), pages 595-609, May.
  4. Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, Elsevier, vol. 38(1), pages 55-70, July.
  5. Hideo Konishi & Utku Unver, 2004. "Credible Group Stability in Multi-Partner Matching Problems," Econometric Society 2004 North American Summer Meetings 32, Econometric Society.
  6. Alvin E. Roth & Elliott Peranson, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," NBER Working Papers 6963, National Bureau of Economic Research, Inc.
  7. Sonmez, T., 1995. "Strategy-Proofness in Many-To-One Matching Problems," Papers, Michigan - Center for Research on Economic & Social Theory 95-01, Michigan - Center for Research on Economic & Social Theory.
  8. 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.
  9. José Alcalde Pérez & Antonio Romero-Medina & David Pérez-Castrillo, 1997. "Hiring procedures to implement stable allocations," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 1997-10, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  10. Echenique, Federico & Oviedo, Jorge, 2002. "Core Many-To-One Matchings by Fixed-Point Methods," Working Papers, California Institute of Technology, Division of the Humanities and Social Sciences 1140, California Institute of Technology, Division of the Humanities and Social Sciences.
  11. 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.
  12. Klijn, F. & Masso, J., 1999. "Weak Stability and a Bargaining Set for the Marriage Model," Discussion Paper, Tilburg University, Center for Economic Research 1999-114, Tilburg University, Center for Economic Research.
  13. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, Econometric Society, vol. 50(6), pages 1483-1504, November.
  14. Adachi, Hiroyuki, 2000. "On a characterization of stable matchings," Economics Letters, Elsevier, vol. 68(1), pages 43-49, July.
  15. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
  16. 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.
  17. 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.
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