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Stable many-to-many matchings with contracts

Author

Listed:
  • 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.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:mateco:v:45:y:2009:i:7-8:p:422-434
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    References listed on IDEAS

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    1. 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.
    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.
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    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 415-440, June.
    12. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
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    Cited by:

    1. repec:eee:gamebe:v:108:y:2018:i:c:p:275-286 is not listed on IDEAS
    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. Antonio Romero-Medina & Matteo Triossi, 2017. "Take-it-or-leave-it contracts in many-to-many matching markets," Documentos de Trabajo 328, Centro de Economía Aplicada, Universidad de Chile.
    4. Tam'as Fleiner & Zsuzsanna Jank'o & Akihisa Tamura & Alexander Teytelboym, 2015. "Trading Networks with Bilateral Contracts," Papers 1510.01210, arXiv.org, revised May 2018.
    5. Kojima, Fuhito, 2013. "Efficient resource allocation under multi-unit demand," Games and Economic Behavior, Elsevier, vol. 82(C), pages 1-14.
    6. Paula Jaramillo & Çaǧatay Kayı & Flip Klijn, 2014. "On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 793-811, April.
    7. John William Hatfield & Charles R. Plott & Tomomi Tanaka, 2012. "Understanding Price Controls and Nonprice Competition with Matching Theory," American Economic Review, American Economic Association, vol. 102(3), pages 371-375, May.
    8. Massó, Jordi & Neme, Alejandro, 2014. "On cooperative solutions of a generalized assignment game: Limit theorems to the set of competitive equilibria," Journal of Economic Theory, Elsevier, vol. 154(C), pages 187-215.
    9. Kominers, Scott Duke, 2012. "On the correspondence of contracts to salaries in (many-to-many) matching," Games and Economic Behavior, Elsevier, vol. 75(2), pages 984-989.
    10. Klijn, Flip & Yazıcı, Ayşe, 2014. "A many-to-many ‘rural hospital theorem’," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 63-73.
    11. Hatfield, John William & Immorlica, Nicole & Kominers, Scott Duke, 2012. "Testing substitutability," Games and Economic Behavior, Elsevier, vol. 75(2), pages 639-645.
    12. Hatfield, John William & Kominers, Scott Duke, 2017. "Contract design and stability in many-to-many matching," Games and Economic Behavior, Elsevier, vol. 101(C), pages 78-97.
    13. Hatfield, John William & Kominers, Scott Duke, 2015. "Multilateral matching," Journal of Economic Theory, Elsevier, vol. 156(C), pages 175-206.
    14. Peter Chen & Michael Egesdal & Marek Pycia & M. Bumin Yenmez, 2016. "Manipulability of Stable Mechanisms," American Economic Journal: Microeconomics, American Economic Association, vol. 8(2), pages 202-214, May.
    15. Westkamp, Alexander, 2010. "Market structure and matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1724-1738, September.
    16. Claus-Jochen Haake & Bettina Klaus, 2009. "Monotonicity and Nash implementation in matching markets with contracts," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 41(3), pages 393-410, December.
    17. M. Bumin Yenmez, 2014. "College Admissions," GSIA Working Papers 2014-E24, Carnegie Mellon University, Tepper School of Business.
    18. Andreas Bjerre-Nielsen, 2015. "Sorting in Networks: Adversity and Structure," Papers 1503.07389, arXiv.org, revised Aug 2017.
    19. Hatfield, John William & Kojima, Fuhito & Narita, Yusuke, 2016. "Improving schools through school choice: A market design approach," Journal of Economic Theory, Elsevier, vol. 166(C), pages 186-211.
    20. repec:eee:jetheo:v:176:y:2018:i:c:p:859-885 is not listed on IDEAS
    21. Bettina Klaus & David F. Manlove & Francesca Rossi, 2014. "Matching under Preferences," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 14.07, Université de Lausanne, Faculté des HEC, DEEP.
    22. Jiao, Zhenhua & Tian, Guoqiang, 2017. "The Blocking Lemma and strategy-proofness in many-to-many matchings," Games and Economic Behavior, Elsevier, vol. 102(C), pages 44-55.
    23. repec:spr:sochwe:v:51:y:2018:i:1:d:10.1007_s00355-018-1108-6 is not listed on IDEAS
    24. Hatfield, John William & Kominers, Scott Duke, 2013. "Vacancies in supply chain networks," Economics Letters, Elsevier, vol. 119(3), pages 354-357.
    25. Jiao, Zhenhua & Tian, Guoqiang, 2015. "The stability of many-to-many matching with max–min preferences," Economics Letters, Elsevier, vol. 129(C), pages 52-56.

    More about this item

    Keywords

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

    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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