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

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Author Info
Echenique, Federico
Oviedo, Jorge

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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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Publisher Info
Paper provided by California Institute of Technology, Division of the Humanities and Social Sciences in its series Working Papers with number 1185.

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Length: 41 pages
Date of creation: Nov 2003
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Publication status: Published: Published in Theoretical Economics 1 (2006) 233-273.
Handle: RePEc:clt:sswopa:1185

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Postal: Working Paper Assistant, Division of the Humanities and Social Sciences, 228-77, Caltech, Pasadena CA 91125
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Related research
Keywords: matching markets; core; lattice; stability; substitutability; Tarski's fixed point theoryem;

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This paper has been announced in the following NEP Reports: References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Adachi, Hiroyuki, 2000. "On a characterization of stable matchings," Economics Letters, Elsevier, vol. 68(1), pages 43-49, July. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
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  3. 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).
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  4. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September. [Downloadable!]
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  5. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May. [Downloadable!] (restricted)
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  6. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
  10. Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 55-70, July. [Downloadable!] (restricted)
  11. 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. [Downloadable!] (restricted)
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  12. Utku Unver & Hideo Konishi, 2005. "Credible Group Stability in Multi-Partner Matching Problems," 2005 Meeting Papers 208, Society for Economic Dynamics. [Downloadable!]
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  13. 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. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  15. Alvin E. Roth & Elliott Peranson, 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. [Downloadable!] (restricted)
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  16. Echenique, Federico & Oviedo, Jorge, 2002. "Core Many-To-One Matchings by Fixed-Point Methods," Working Papers 1140, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Claus-Jochen Haake & Bettina Klaus, 2009. "Monotonicity and Nash implementation in matching markets with contracts," Economic Theory, Springer, vol. 41(3), pages 393-410, December. [Downloadable!] (restricted)
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  2. Hideo Konishi & M. Utku Ünver, 2003. "Credible Group Stability in Multi-Partner Matching Problems," Working Papers 2003.115, Fondazione Eni Enrico Mattei. [Downloadable!]
    Other versions:
  3. Roland Pongou & Roberto Serrano, 2009. "A Dynamic Theory of Fidelity Networks with an Application to the Spread of HIV/AIDS," Working Papers 2009-2, Brown University, Department of Economics. [Downloadable!]
    Other versions:
  4. Bettina-Elisabeth Klaus & Markus Walzl, 2007. "Stable Many-to-Many Matchings with Contracts," Harvard Business School Working Papers 09-046, Harvard Business School, revised Sep 2008. [Downloadable!]
    Other versions:
  5. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2006. "Farsightedly Stable Networks," Research Memoranda 041, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
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  6. Robin S. Lee & Michael Schwarz, 2009. "Interviewing in Two-Sided Matching Markets," NBER Working Papers 14922, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  7. Alvin Roth, 2008. "Deferred acceptance algorithms: history, theory, practice, and open questions," International Journal of Game Theory, Springer, vol. 36(3), pages 537-569, March. [Downloadable!] (restricted)
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  8. Echenique, Federico & Yenmez, Mehmet B., 2005. "A Solution to Matching with Preferences over Colleagues," Working Papers 1226, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
    Other versions:
  9. Fuhito Kojima & M. Ünver, 2008. "Random paths to pairwise stability in many-to-many matching problems: a study on market equilibration," International Journal of Game Theory, Springer, vol. 36(3), pages 473-488, March. [Downloadable!] (restricted)
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