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A solution to matching with preferences over colleagues

  • Echenique, Federico
  • Yenmez, M. Bumin

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.sciencedirect.com/science/article/B6WFW-4KW5WGN-1/2/396d92b020d8619afc95f0c1b60a953a
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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 59 (2007)
Issue (Month): 1 (April)
Pages: 46-71

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Handle: RePEc:eee:gamebe:v:59:y:2007:i:1:p:46-71
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. 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.
  2. 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.
  3. Federico Echenique & Jorge Oviedo, 2004. "A Theory of Stability in Many-to-many Matching Markets," Game Theory and Information 0401002, EconWPA.
  4. Federico Echenique, 2004. "Counting Combinatorial Choice Rules," Game Theory and Information 0404004, EconWPA.
  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. Bettina Klaus & Flip Klijn, 2004. "Stable Matchings and Preferences of Couples," Working Papers 117, Barcelona Graduate School of Economics.
  7. Adachi, Hiroyuki, 2000. "On a characterization of stable matchings," Economics Letters, Elsevier, vol. 68(1), pages 43-49, July.
  8. 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.
  9. 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.
  10. 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.
  11. Pablo Revilla, 2007. "Many-to-One Matching when Colleagues Matter," Working Papers 2007.87, Fondazione Eni Enrico Mattei.
  12. 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.
  13. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
  14. 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.
  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. 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.
  17. Michael Ostrovsky, 2008. "Stability in Supply Chain Networks," American Economic Review, American Economic Association, vol. 98(3), pages 897-923, June.
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