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Stable many-to-many matchings with contracts

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  • 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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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/jmateco

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

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References

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  1. Hideo Konishi & M. Utku Ünver, 2003. "Credible Group Stability in Many-to-Many Matching Problems," Game Theory and Information, EconWPA 0309005, EconWPA, revised 06 Sep 2003.
  2. Roth, Alvin E, 1986. "On the Allocation of Residents to Rural Hospitals: A General Property of Two-Sided Matching Markets," Econometrica, Econometric Society, Econometric Society, vol. 54(2), pages 425-27, March.
  3. Bettina Klaus & Flip Klijn & Toshifumi Nakamura, 2007. "Corrigendum: Stable Matchings and Preferences of Couples," UFAE and IAE Working Papers, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) 708.07, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  4. Paul Milgrom, 2003. "Matching with Contracts," Working Papers, Stanford University, Department of Economics 03003, Stanford University, Department of Economics.
  5. Bettina-Elisabeth Klaus & Markus Walzl, 2007. "Stable Many-to-Many Matchings with Contracts," Harvard Business School Working Papers, Harvard Business School 09-046, Harvard Business School, revised Sep 2008.
  6. Echenique, Federico & Oviedo, Jorge, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, Econometric Society, vol. 1(2), pages 233-273, June.
  7. 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, American Economic Association, vol. 81(3), pages 415-40, June.
  8. 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.
  9. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, Econometric Society, vol. 52(1), pages 47-57, January.
  10. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, Elsevier, vol. 121(1), pages 75-106, March.
  11. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, Elsevier, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
  12. 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.
  13. 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, University of Chicago Press, vol. 92(6), pages 991-1016, December.
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Citations

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Cited by:
  1. Claus-Jochen Haake & Bettina Klaus, 2005. "Monotonicity and Nash implementation in matching markets with contracts," Working Papers, Bielefeld University, Center for Mathematical Economics 372, Bielefeld University, Center for Mathematical Economics.
  2. Paula Jaramillo & Çagatay Kayi & Flip Klijn, 2012. "On the Exhaustiveness of Truncation and Dropping Strategies in Many-to-Many Matching Markets," Working Papers, Barcelona Graduate School of Economics 632, Barcelona Graduate School of Economics.
  3. Kojima, Fuhito, 2013. "Efficient resource allocation under multi-unit demand," Games and Economic Behavior, Elsevier, Elsevier, vol. 82(C), pages 1-14.
  4. Kominers, Scott Duke, 2012. "On the correspondence of contracts to salaries in (many-to-many) matching," Games and Economic Behavior, Elsevier, Elsevier, vol. 75(2), pages 984-989.
  5. Bettina-Elisabeth Klaus & Markus Walzl, 2007. "Stable Many-to-Many Matchings with Contracts," Harvard Business School Working Papers, Harvard Business School 09-046, Harvard Business School, revised Sep 2008.
  6. Hatfield, John William & Immorlica, Nicole & Kominers, Scott Duke, 2012. "Testing substitutability," Games and Economic Behavior, Elsevier, Elsevier, vol. 75(2), pages 639-645.
  7. Westkamp, Alexander, 2010. "Market structure and matching with contracts," Journal of Economic Theory, Elsevier, Elsevier, vol. 145(5), pages 1724-1738, September.
  8. Hatfield, John William & Kominers, Scott Duke, 2013. "Vacancies in supply chain networks," Economics Letters, Elsevier, Elsevier, vol. 119(3), pages 354-357.
  9. John William Hatfield & Charles R. Plott & Tomomi Tanaka, 2012. "Understanding Price Controls and Nonprice Competition with Matching Theory," American Economic Review, American Economic Association, American Economic Association, vol. 102(3), pages 371-75, May.

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