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Stable Many-to-Many Matchings with Contracts

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  • Klaus, Bettina
  • Walzl, Markus

    (METEOR)

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 stable sets and pairwise stable sets for general, substitutable, and strongly substitutable preferences. Apart from obtaining “set inclusion results'''' on all three domains, we 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. We also show that Roth’s (1984) stability coincides with pairwise stability for substitutable preferences.

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Bibliographic Info

Paper provided by Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) in its series Research Memorandum with number 042.

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Date of creation: 2006
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Handle: RePEc:unm:umamet:2006042

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Keywords: microeconomics ;

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References

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  1. Klaus, Bettina & Walzl, Markus, 2006. "Stable Many-to-Many Matchings with Contracts," Research Memorandum, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) 042, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Echenique, Federico & Oviedo, Jorge, 2003. "A Theory of Stability in Many-to-Many Matching Markets," Working Papers, California Institute of Technology, Division of the Humanities and Social Sciences 1185, California Institute of Technology, Division of the Humanities and Social Sciences.
  3. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, American Economic Association, vol. 95(4), pages 913-935, September.
  4. Konishi, Hideo & Unver, M. Utku, 2006. "Credible group stability in many-to-many matching problems," Journal of Economic Theory, Elsevier, Elsevier, vol. 129(1), pages 57-80, July.
  5. 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.
  6. Bettina Klaus & Flip Klijn, 2004. "Stable Matchings and Preferences of Couples," Working Papers 117, Barcelona Graduate School of Economics.
  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. Bettina Klaus & Flip Klijn & Toshifumi Nakamura, 2005. "Corrigendum: Stable Matchings and Preferences of Couples," Working Papers 261, Barcelona Graduate School of Economics.
  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. 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.
  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. 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.
  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. Westkamp, Alexander, 2010. "Market structure and matching with contracts," Journal of Economic Theory, Elsevier, Elsevier, vol. 145(5), pages 1724-1738, September.
  2. 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.
  3. Hatfield, John William & Kominers, Scott Duke, 2013. "Vacancies in supply chain networks," Economics Letters, Elsevier, Elsevier, vol. 119(3), pages 354-357.
  4. Haake,Claus-Jochen & Klaus,Bettina, 2005. "Monotonicity and Nash Implementation in Matching Markets with Contracts," Research Memorandum, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) 028, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  5. Paula Jaramillo & Çagatay Kayi & Flip Klijn, 2012. "On the Exhaustiveness of Truncation and Dropping Strategies in Many-to-Many Matching Markets," Working Papers 632, Barcelona Graduate School of Economics.
  6. Kojima, Fuhito, 2013. "Efficient resource allocation under multi-unit demand," Games and Economic Behavior, Elsevier, Elsevier, vol. 82(C), pages 1-14.
  7. 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.
  8. 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.
  9. Hatfield, John William & Immorlica, Nicole & Kominers, Scott Duke, 2012. "Testing substitutability," Games and Economic Behavior, Elsevier, Elsevier, vol. 75(2), pages 639-645.

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