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Stable many-to-many matchings with contracts

Author Info

  • 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;

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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. 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 415-40, June.
  2. Federico Echenique & Jorge Oviedo, 2004. "A Theory of Stability in Many-to-many Matching Markets," Game Theory and Information 0401002, EconWPA.
  3. Paul Milgrom, 2003. "Matching with Contracts," Working Papers 03003, Stanford University, Department of Economics.
  4. Hideo Konishi & M. Utku Ünver, 2003. "Credible Group Stability in Many-to-Many Matching Problems," Game Theory and Information 0309005, EconWPA, revised 06 Sep 2003.
  5. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
  6. 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 425-27, March.
  7. 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.
  8. Klaus Bettina & Klijn Flip & Nakamura Toshifumi, 2007. "Corrigendum: Stable Matchings and Preferences of Couples," Research Memorandum 025, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  9. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
  10. 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.
  11. Bettina Klaus & Flip Klijn, 2004. "Stable Matchings and Preferences of Couples," Working Papers 117, Barcelona Graduate School of Economics.
  12. 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.
  13. Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 55-70, July.
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