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A Solution to Matching with Preferences over Colleagues

Author Info

  • Echenique, Federico
  • Yenmez, Mehmet B.

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://www.hss.caltech.edu/SSPapers/sswp1226c.pdf
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Paper provided by California Institute of Technology, Division of the Humanities and Social Sciences in its series Working Papers with number 1226.

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Length: 25 pages
Date of creation: Jun 2005
Date of revision:
Publication status: Published in Games and Economic Behavior 59 (2007) 46-71.
Handle: RePEc:clt:sswopa:1226
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Keywords: matching markets; core; lattice; Gale-Shapley algorithm;

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Find related papers by JEL classification:
  • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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  1. Federico Echenique & Jorge Oviedo, 2003. "Core Many-to-one Matchings by Fixed-point Methods," Game Theory and Information 0302001, EconWPA.
  2. Michael Ostrovsky, 2008. "Stability in Supply Chain Networks," American Economic Review, American Economic Association, vol. 98(3), pages 897-923, June.
  3. Pablo Revilla, 2007. "Many-to-One Matching when Colleagues Matter," Working Papers 2007.87, Fondazione Eni Enrico Mattei.
  4. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, vol. 121(1), pages 75-106, March.
  5. Jorge Oviedo & Federico Echenique, 2005. "A Theory of Stability in Many-to-Many Matching Markets," 2005 Meeting Papers 233, Society for Economic Dynamics.
  6. 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.
  7. 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.
  8. Federico Echenique, 2004. "Counting Combinatorial Choice Rules," Game Theory and Information 0404004, EconWPA.
  9. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
  10. Bettina Klaus & Flip Klijn, 2005. "Corrigendum: Stable Matchings and Preferences of Couples," UFAE and IAE Working Papers 653.05, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  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. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
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