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Core Many-to-one Matchings by Fixed-point Methods

Author

Listed:
  • Federico Echenique

    (Caltech)

  • Jorge Oviedo

    (Universidad de San Luis)

Abstract

We characterize the core many-to-one matchings as fixed points of a map. Our characterization gives an algorithm for finding core allocations; the algorithm is efficient and simple to implement. Our characterization does not require substitutable preferences, so it is separate from the structure needed for the non-emptiness of the core. When preferences are substitutable, our characterization gives a simple proof of the lattice structure of core matchings, and it gives a method for computing the join and meet of two core matchings.

Suggested Citation

  • Federico Echenique & Jorge Oviedo, 2003. "Core Many-to-one Matchings by Fixed-point Methods," Game Theory and Information 0302001, EconWPA.
  • Handle: RePEc:wpa:wuwpga:0302001
    Note: Type of Document - PDF; prepared on Linux PC; to print on PostScript; pages: 30
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    References listed on IDEAS

    as
    1. Roth, Alvin E. & Sotomayor, Marilda, 1988. "Interior points in the core of two-sided matching markets," Journal of Economic Theory, Elsevier, vol. 45(1), pages 85-101, June.
    2. Ahmet Alkan, 2002. "A class of multipartner matching markets with a strong lattice structure," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 737-746.
    3. Adachi, Hiroyuki, 2000. "On a characterization of stable matchings," Economics Letters, Elsevier, vol. 68(1), pages 43-49, July.
    4. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
    5. Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 55-70, July.
    6. 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.
    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.
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    Citations

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    Cited by:

    1. Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
    2. Alvin Roth, 2008. "Deferred acceptance algorithms: history, theory, practice, and open questions," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 537-569, March.
    3. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    4. Echenique, Federico & Oviedo, Jorge, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, vol. 1(2), pages 233-273, June.
    5. Abizada, Azar, 2016. "Stability and incentives for college admissions with budget constraints," Theoretical Economics, Econometric Society, vol. 11(2), May.
    6. Kucuksenel, Serkan, 2011. "Core of the assignment game via fixed point methods," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 72-76, January.
    7. Schlegel, Jan Christoph, 2015. "Contracts versus salaries in matching: A general result," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 552-573.
    8. Echenique, Federico & Yenmez, M. Bumin, 2007. "A solution to matching with preferences over colleagues," Games and Economic Behavior, Elsevier, vol. 59(1), pages 46-71, April.
    9. Bando, Keisuke, 2014. "A modified deferred acceptance algorithm for many-to-one matching markets with externalities among firms," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 173-181.
    10. David Cantala, 2002. "Agreement toward stability in senior matching markets," Department of Economics and Finance Working Papers EC200201, Universidad de Guanajuato, Department of Economics and Finance, revised Jun 2007.
    11. Martínez, Ruth & Massó, Jordi & Neme, Alejandro & Oviedo, Jorge, 2012. "On the invariance of the set of Core matchings with respect to preference profiles," Games and Economic Behavior, Elsevier, vol. 74(2), pages 588-600.
    12. Hakan İnal, 2015. "Core of coalition formation games and fixed-point methods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 745-763, December.
    13. David Cantala, 2011. "Agreement toward stability in matching markets," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 293-316, December.
    14. Juan Cesco, 2012. "Hedonic games related to many-to-one matching problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 737-749, October.
    15. 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.
    16. Vilmos Komornik & Christelle Viauroux, 2012. "Conditional Stable Matchings," UMBC Economics Department Working Papers 12-03, UMBC Department of Economics.
    17. Bando, Keisuke, 2012. "Many-to-one matching markets with externalities among firms," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 14-20.
    18. repec:eee:ecolet:v:156:y:2017:i:c:p:65-67 is not listed on IDEAS
    19. repec:spr:jogath:v:46:y:2017:i:3:d:10.1007_s00182-016-0564-4 is not listed on IDEAS
    20. Hatfield, John William & Kojima, Fuhito, 2010. "Substitutes and stability for matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1704-1723, September.
    21. Roessler, Christian & Koellinger, Philipp, 2012. "Entrepreneurship and organization design," European Economic Review, Elsevier, vol. 56(4), pages 888-902.
    22. David Cantala & Francisco Sánchez, 2008. "Welfare and stability in senior matching markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 369-392, March.
    23. Tam'as Fleiner & Zsuzsanna Jank'o & Akihisa Tamura & Alexander Teytelboym, 2015. "Trading Networks with Bilateral Contracts," Papers 1510.01210, arXiv.org, revised May 2018.
    24. EHLERS, Lars, 2010. "School Choice with Control," Cahiers de recherche 2010-05, Universite de Montreal, Departement de sciences economiques.
    25. Jan Christoph Schlegel, 2014. "Contracts versus Salaries in Matching: A General Result. N.B.: This paper replaces Nr 13.09 "Contracts versus Salaries in Matching: Comment", (June 2013)," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 14.05, Université de Lausanne, Faculté des HEC, DEEP.

    More about this item

    Keywords

    matching; supermodular games; tarski's fixed-point theorem;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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