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Stable Many-to-Many Matchings with Contracts

  • Bettina-Elisabeth Klaus


    (Harvard Business School, Negotiation, Organizations & Markets Unit)

  • Markus Walzl


    (School of Economics and Management, Free University of Bozen/Bolzano, Italy)

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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Paper provided by Harvard Business School in its series Harvard Business School Working Papers with number 09-046.

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Length: 25 pages
Date of creation: Aug 2007
Date of revision: Sep 2008
Handle: RePEc:hbs:wpaper:09-046
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  1. 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.
  2. Echenique, Federico & Oviedo, Jorge, 2003. "A Theory of Stability in Many-to-Many Matching Markets," Working Papers 1185, California Institute of Technology, Division of the Humanities and Social Sciences.
  3. Bettina Klaus & Flip Klijn & Toshifumi Nakamura, 2005. "Corrigendum: Stable Matchings and Preferences of Couples," Working Papers 261, Barcelona Graduate School of Economics.
  4. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, vol. 121(1), pages 75-106, March.
  5. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882.
  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. 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.
  8. 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.
  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. Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 55-70, July.
  11. 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.
  12. Paul Milgrom, 2003. "Matching with Contracts," Working Papers 03003, Stanford University, Department of Economics.
  13. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
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