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Substitutes and stability for matching with contracts

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  • Hatfield, John William
  • Kojima, Fuhito
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    Abstract

    We consider the matching with contracts framework of Hatfield and Milgrom [20], and we introduce new concepts of bilateral and unilateral substitutes. We show that the bilateral substitutes condition is a sufficient condition for the existence of a stable allocation in this framework. However, the set of stable allocations does not form a lattice under this condition, and there does not necessarily exist a doctor-optimal stable allocation. Under a slightly stronger condition, unilateral substitutes, the set of stable allocations still does not necessarily form a lattice with respect to doctors' preferences, but there does exist a doctor-optimal stable allocation, and other key results such as incentive compatibility and the rural hospitals theorem are recovered.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Economic Theory.

    Volume (Year): 145 (2010)
    Issue (Month): 5 (September)
    Pages: 1704-1723

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    Handle: RePEc:eee:jetheo:v:145:y:2010:i:5:p:1704-1723

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    Web page: http://www.elsevier.com/locate/inca/622869

    Related research

    Keywords: Substitutes Bilateral substitutes Unilateral substitutes Matching Matching with contracts Law of aggregate demand Stability Strategy-proofness Rural hospitals theorem Group strategy-proofness Lattice;

    References

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    1. Hideo Konishi & M. Utku Unver, 2003. "Credible Group-Stability in Many-to-Many Matching Problems," Boston College Working Papers in Economics 570, Boston College Department of Economics, revised 19 Jan 2005.
    2. Michael Ostrovsky, 2008. "Stability in Supply Chain Networks," American Economic Review, American Economic Association, vol. 98(3), pages 897-923, June.
    3. 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.
    4. Ruth Martínez & Jordi Massó & Alejdanro Neme & Jorge Oviedo, 2004. "On group strategy-proof mechanisms for a many-to-one matching model," International Journal of Game Theory, Springer, vol. 33(1), pages 115-128, January.
    5. Bettina Klaus & Flip Klijn & Toshifumi Nakamura, 2007. "Corrigendum: Stable Matchings and Preferences of Couples," UFAE and IAE Working Papers 708.07, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    6. Ahmet Alkan, 2002. "A class of multipartner matching markets with a strong lattice structure," Economic Theory, Springer, vol. 19(4), pages 737-746.
    7. Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2000. "Single Agents and the Set of Many-to-One Stable Matchings," Journal of Economic Theory, Elsevier, vol. 91(1), pages 91-105, March.
    8. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    9. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
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    11. 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.
    12. Elliott Peranson & Alvin E. Roth, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," American Economic Review, American Economic Association, vol. 89(4), pages 748-780, September.
    13. Echenique, Federico & Oviedo, Jorge, 2002. "Core Many-To-One Matchings by Fixed-Point Methods," Working Papers 1140, California Institute of Technology, Division of the Humanities and Social Sciences.
    14. 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.
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    16. Alvin E. Roth & Uriel G. Rothblum, 1999. "Truncation Strategies in Matching Markets--In Search of Advice for Participants," Econometrica, Econometric Society, vol. 67(1), pages 21-44, January.
    17. Hatfield, John William & Kojima, Fuhito, 2009. "Group incentive compatibility for matching with contracts," Games and Economic Behavior, Elsevier, vol. 67(2), pages 745-749, November.
    18. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, vol. 121(1), pages 75-106, March.
    19. Roth, Alvin E & Vande Vate, John H, 1991. "Incentives in Two-Sided Matching with Random Stable Mechanisms," Economic Theory, Springer, vol. 1(1), pages 31-44, January.
    20. Kojima, Fuhito, 2008. "The law of aggregate demand and welfare in the two-sided matching market," Economics Letters, Elsevier, vol. 99(3), pages 581-584, June.
    21. Paul Milgrom, 2003. "Matching with Contracts," Working Papers 03003, Stanford University, Department of Economics.
    22. Atila Abdulkadiroğlu, 2005. "College admissions with affirmative action," International Journal of Game Theory, Springer, vol. 33(4), pages 535-549, November.
    23. Pathak, Parag A. & Abdulkadiroglu, Atila & Roth, Alvin, 2005. "The New York City High School Match," Scholarly Articles 2562765, Harvard University Department of Economics.
    24. Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, vol. 99(3), pages 608-27, June.
    25. Ausubel Lawrence M & Milgrom Paul R, 2002. "Ascending Auctions with Package Bidding," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-44, August.
    26. Klaus, Bettina & Klijn, Flip & Nakamura, Toshifumi, 2009. "Corrigendum to "Stable matchings and preferences of couples" [J. Econ. Theory 121 (1) (2005) 75-106]," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2227-2233, September.
    27. Adachi, Hiroyuki, 2000. "On a characterization of stable matchings," Economics Letters, Elsevier, vol. 68(1), pages 43-49, July.
    28. 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.
    29. John William Hatfield & Fuhito Kojima, 2008. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 98(3), pages 1189-94, June.
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    Citations

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    Cited by:
    1. Orhan Aygün & Tayfun Sönmez, 2012. "The Importance of Irrelevance of Rejected Contracts in Matching under Weakened Substitutes Conditions," Boston College Working Papers in Economics 805, Boston College Department of Economics.
    2. Flip Klijn, 2011. "A Many-to-Many 'Rural Hospital Theorem'," UFAE and IAE Working Papers 877.11, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    3. Hatfield, John William & Immorlica, Nicole & Kominers, Scott Duke, 2012. "Testing substitutability," Games and Economic Behavior, Elsevier, vol. 75(2), pages 639-645.
    4. Tayfun Sönmez & Tobias B. Switzer, 2011. "Matching with (Branch-of-Choice) Contracts at United States Military Academy," Boston College Working Papers in Economics 782, Boston College Department of Economics.
    5. Tayfun Sönmez, 2011. "Bidding for Army Career Specialties: Improving the ROTC Branching Mechanism," Boston College Working Papers in Economics 783, Boston College Department of Economics.
    6. Peter Biro & Flip Klijn, 2011. "Matching with Couples: a Multidisciplinary Survey," IEHAS Discussion Papers 1139, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
    7. John William Hatfield & Scott Duke Kominers, 2012. "Matching in Networks with Bilateral Contracts," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 176-208, February.
    8. Orhan Aygün & Tayfun Sönmez, 2012. "Matching with Contracts: The Critical Role of Irrelevance of Rejected Contracts," Boston College Working Papers in Economics 804, Boston College Department of Economics.
    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. Toyotaka Sakai, 2011. "A note on strategy-proofness from the doctor side in matching with contracts," Review of Economic Design, Springer, vol. 15(4), pages 337-342, December.
    11. Federico Echenique, 2012. "Contracts versus Salaries in Matching," American Economic Review, American Economic Association, vol. 102(1), pages 594-601, February.
    12. Yang, Yi-You, 2013. "A classification approach to Walrasian equilibrium with substitutability," MPRA Paper 47945, University Library of Munich, Germany.
    13. Jan Christoph Schlegel, 2013. "Contracts versus Salaries in Matching: Comment," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 13.09, Université de Lausanne, Faculté des HEC, DEEP.
    14. Umut M. Dur & Scott Duke Kominers & Parag A. Pathak & Tayfun Sönmez, 2013. "The Demise of Walk Zones in Boston: Priorities vs. Precedence in School Choice," NBER Working Papers 18981, National Bureau of Economic Research, Inc.

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