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Stable many-to-many matchings with contracts

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Listed author(s):
  • Klaus, Bettina
  • Walzl, Markus

Abstract

We consider several notions of setwise stability for many-to-many matching markets with contracts and provide an analysis of the relations between the resulting sets of stable allocations for general, substitutable, and strongly substitutable preferences. Apart from obtaining "set inclusion results" on all three domains, we introduce weak setwise stability as a new stability concept and prove that for substitutable preferences the set of pairwise stable matchings is nonempty and coincides with the set of weakly setwise stable matchings. For strongly substitutable preferences the set of pairwise stable matchings coincides with the set of setwise stable matchings.

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File URL: http://www.sciencedirect.com/science/article/pii/S0304-4068(09)00021-4
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Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 45 (2009)
Issue (Month): 7-8 (July)
Pages: 422-434

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Handle: RePEc:eee:mateco:v:45:y:2009:i:7-8:p:422-434
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

Keywords: Many-to-many matching Matching with contracts Pairwise stability Setwise stability;

Other versions of this item:

Find related papers by JEL classification:
  • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
  • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
  • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
  • J41 - Labor and Demographic Economics - - Particular Labor Markets - - - Labor Contracts

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  1. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, vol. 121(1), pages 75-106, March.
  2. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882, February.
  3. Konishi, Hideo & Unver, M. Utku, 2006. "Credible group stability in many-to-many matching problems," Journal of Economic Theory, Elsevier, vol. 129(1), pages 57-80, July.
  4. Klaus, Bettina & Walzl, Markus, 2009. "Stable many-to-many matchings with contracts," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 422-434, July.
  5. Bettina Klaus & Flip Klijn & Toshifumi Nakamura, 2005. "Corrigendum: Stable Matchings and Preferences of Couples," Working Papers 261, Barcelona Graduate School of Economics.
  6. Echenique, Federico & Oviedo, Jorge, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, vol. 1(2), pages 233-273, June.
  7. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
  8. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
  9. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
  10. Roth, Alvin E, 1986. "On the Allocation of Residents to Rural Hospitals: A General Property of Two-Sided Matching Markets," Econometrica, Econometric Society, vol. 54(2), pages 425-427, March.
  11. Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 55-70, July.
  12. 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.
  13. Roth, Alvin E, 1991. "A Natural Experiment in the Organization of Entry-Level Labor Markets: Regional Markets for New Physicians and Surgeons in the United Kingdom," American Economic Review, American Economic Association, vol. 81(3), pages 415-440, June.
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