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A Solution to Matching with Preferences over Colleagues

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  • 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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  1. Dutta, B. & Masso, J., 1996. "Stability of Matchings when Individuals Have Preferences Over Colleagues," UFAE and IAE Working Papers 325.96, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. 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.
  3. 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.
  4. Echenique, Federico, 2004. "Counting Combinatoral Choice Rules," Working Papers 1199, California Institute of Technology, Division of the Humanities and Social Sciences.
  5. Suryapratim Banerjee & Hideo Konishi & Tayfun Sonmez, 1999. "Core in a Simple Coalition Formation Game," Boston College Working Papers in Economics 449, Boston College Department of Economics.
  6. Bettina Klaus & Flip Klijn, 2004. "Stable Matchings and Preferences of Couples," Working Papers 117, Barcelona Graduate School of Economics.
  7. Federico Echenique & Jorge Oviedo, 2004. "A Theory of Stability in Many-to-many Matching Markets," Game Theory and Information 0401002, EconWPA.
  8. Pablo Revilla, 2004. "Many-to-one Matching When Colleagues Matter," Economic Working Papers at Centro de Estudios Andaluces E2004/85, Centro de Estudios Andaluces.
  9. Klaus, Bettina & Klijn, Flip & Nakamura, Toshifumi, 2007. "Corrigendum: Stable Matchings and Preferences of Couples," Research Memorandum 025, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  10. Adachi, Hiroyuki, 2000. "On a characterization of stable matchings," Economics Letters, Elsevier, vol. 68(1), pages 43-49, July.
  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. 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.
  13. Michael Ostrovsky, 2008. "Stability in Supply Chain Networks," American Economic Review, American Economic Association, vol. 98(3), pages 897-923, June.
  14. 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.
  15. 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.
  16. 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.
  17. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
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Citations

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Cited by:
  1. Bando, Keisuke, 2012. "Many-to-one matching markets with externalities among firms," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 14-20.
  2. Kucuksenel, Serkan, 2011. "Core of the assignment game via fixed point methods," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 72-76, January.
  3. 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.
  4. Alvin Roth, 2008. "Deferred acceptance algorithms: history, theory, practice, and open questions," International Journal of Game Theory, Springer, vol. 36(3), pages 537-569, March.
  5. repec:pdn:wpaper:74 is not listed on IDEAS
  6. Mumcu, Ayse & Saglam, Ismail, 2010. "Stable one-to-one matchings with externalities," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 154-159, September.
  7. Pablo Revilla, 2004. "Many-to-one Matching When Colleagues Matter," Economic Working Papers at Centro de Estudios Andaluces E2004/85, Centro de Estudios Andaluces.
  8. Ana Mauleon & Nils Roehl & Vincent Vannetelbosch, 2014. "Constitutions and Social Networks," Working Papers CIE 74, University of Paderborn, CIE Center for International Economics.
  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, 2006. "One-to-One Matching with Interdependent Preferences," MPRA Paper 1908, University Library of Munich, Germany.
  11. Kominers, Scott Duke, 2010. "Matching with preferences over colleagues solves classical matching," Games and Economic Behavior, Elsevier, vol. 68(2), pages 773-780, March.
  12. Emiliya Lazarova & Dinko Dimitrov, 2013. "Status-seeking in hedonic games with heterogeneous players," Social Choice and Welfare, Springer, vol. 40(4), pages 1205-1229, April.
  13. Dimitrov, Dinko & Lazarova, Emiliya, 2011. "Two-sided coalitional matchings," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 46-54, July.
  14. Ismail Saglam & Ayse Mumcu, 2007. "The core of a housing market with externalities," Economics Bulletin, AccessEcon, vol. 3(57), pages 1-5.
  15. repec:ebl:ecbull:v:3:y:2007:i:57:p:1-5 is not listed on IDEAS
  16. Vilmos Komornik & Christelle Viauroux, 2012. "Conditional Stable Matchings," UMBC Economics Department Working Papers 12-03, UMBC Department of Economics.
  17. Dinko Dimitrov & Emiliya Lazarova, 2008. "Coalitional Matchings," Working Papers 2008.45, Fondazione Eni Enrico Mattei.

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