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A Solution to Matching with Preferences over Colleagues

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Author Info

  • Federico Echenique

    (California Institute of Technology)

Abstract

We study many-to-one matchings, such as the assignment of students to colleges, where the students have preferences over the other students who would attend the same college. It is well known that the core of this model may be empty, without strong assumptions on agents' preferences. We introduce a method that finds all core matchings, if any exist. The method requires no assumptions on preferences. Our method also finds certain partial solutions that may be useful when the core is empty.

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File URL: http://128.118.178.162/eps/game/papers/0506/0506005.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Game Theory and Information with number 0506005.

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Length: 28 pages
Date of creation: 20 Jun 2005
Date of revision:
Handle: RePEc:wpa:wuwpga:0506005

Note: Type of Document - pdf; pages: 28
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Web page: http://128.118.178.162

Related research

Keywords: Two-sided Matching; Core; Externalities; Lattice; Tarski's Fixed Point Theorem; Gale-Shapley Algorithm;

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References

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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  1. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer, vol. 18(1), pages 135-153.
  2. Pablo Revilla, 2004. "Many-to-one Matching When Colleagues Matter," Economic Working Papers at Centro de Estudios Andaluces E2004/85, Centro de Estudios Andaluces.
  3. 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).
  4. 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.
  5. Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2004. "An algorithm to compute the full set of many-to-many stable matchings," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 187-210, March.
  6. Echenique, Federico & Oviedo, Jorge, 2004. "Core many-to-one matchings by fixed-point methods," Journal of Economic Theory, Elsevier, vol. 115(2), pages 358-376, April.
  7. 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.
  8. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, vol. 121(1), pages 75-106, March.
  9. Federico Echenique, 2004. "Counting Combinatorial Choice Rules," Game Theory and Information 0404004, EconWPA.
  10. Michael Ostrovsky, 2008. "Stability in Supply Chain Networks," American Economic Review, American Economic Association, vol. 98(3), pages 897-923, June.
  11. Greenberg, Joseph, 1994. "Coalition structures," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 37, pages 1305-1337 Elsevier.
  12. Adachi, Hiroyuki, 2000. "On a characterization of stable matchings," Economics Letters, Elsevier, vol. 68(1), pages 43-49, July.
  13. Dutta, Bhaskar & Masso, Jordi, 1997. "Stability of Matchings When Individuals Have Preferences over Colleagues," Journal of Economic Theory, Elsevier, vol. 75(2), pages 464-475, August.
  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.
  15. McKelvey, Richard D. & McLennan, Andrew, 1996. "Computation of equilibria in finite games," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 2, pages 87-142 Elsevier.
  16. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
  17. Von Stengel, Bernhard, 2002. "Computing equilibria for two-person games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 45, pages 1723-1759 Elsevier.
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Citations

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Cited by:
  1. Alvin E. Roth, 2007. "Deferred Acceptance Algorithms: History, Theory, Practice, and Open Questions," NBER Working Papers 13225, National Bureau of Economic Research, Inc.
  2. Dinko Dimitrov & Emiliya Lazarova, 2008. "Coalitional Matchings," Working Papers 2008.45, Fondazione Eni Enrico Mattei.
  3. repec:ebl:ecbull:v:3:y:2007:i:57:p:1-5 is not listed on IDEAS
  4. Pablo Revilla, 2007. "Many-to-One Matching when Colleagues Matter," Working Papers 2007.87, Fondazione Eni Enrico Mattei.
  5. Ana Mauleon & Nils Roehl & Vincent Vannetelbosch, 2014. "Constitutions and Social Networks," Working Papers 74, University of Paderborn, CIE Center for International Economics.
  6. Emiliya Lazarova & Dinko Dimitrov, 2010. "Status-Seeking in Hedonic Games with Heterogeneous Players," Working Papers 2010.122, Fondazione Eni Enrico Mattei.
  7. Kominers, Scott Duke, 2010. "Matching with preferences over colleagues solves classical matching," Games and Economic Behavior, Elsevier, vol. 68(2), pages 773-780, March.
  8. Dimitrov, Dinko & Lazarova, Emiliya, 2011. "Two-sided coalitional matchings," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 46-54, July.
  9. Federico Echenique & SangMok Lee & M. Bumin Yenmez, 2010. "Existence and Testable Implications of Extreme Stable Matchings," Levine's Working Paper Archive 661465000000000337, David K. Levine.
  10. Mumcu, Ayse & Saglam, Ismail, 2010. "Stable one-to-one matchings with externalities," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 154-159, September.
  11. Mumcu, Ayse & Saglam, Ismail, 2006. "One-to-One Matching with Interdependent Preferences," MPRA Paper 1908, University Library of Munich, Germany.
  12. Vilmos Komornik & Christelle Viauroux, 2012. "Conditional Stable Matchings," UMBC Economics Department Working Papers 12-03, UMBC Department of Economics.
  13. Bando, Keisuke, 2012. "Many-to-one matching markets with externalities among firms," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 14-20.
  14. Kucuksenel, Serkan, 2011. "Core of the assignment game via fixed point methods," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 72-76, January.

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