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Smith and Rawls Share a Room: Stability and Medians

  • Bettina Klaus


    (Harvard Business School, Negotiation, Organizations & Markets Unit)

  • Flip Klijn


    (Institute for Economic Analysis (CSIC), Campus UAB, Barcelona, Spain)

We consider one-to-one, one-sided matching (roommate) problems in which agents can either be matched as pairs or remain single. We introduce a so-called bi-choice graph for each pair of stable matchings and characterize its structure. Exploiting this structure we obtain as a corollary the "lone wolf" theorem and a decomposability result. The latter result together with transitivity of blocking leads to an elementary proof of the so-called stable median matching theorem, showing how the often incompatible concepts of stability (represented by the political economist Adam Smith) and fairness (represented by the political philosopher John Rawls) can be reconciled for roommate problems. Finally, we extend our results to two-sided matching problems.

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Paper provided by Harvard Business School in its series Harvard Business School Working Papers with number 09-111.

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Length: 23 pages
Date of creation: Feb 2009
Date of revision:
Handle: RePEc:hbs:wpaper:09-111
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  1. 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.
  2. Michael Schwarz & M. Bumin Yenmez, 2009. "Median Stable Matching," NBER Working Papers 14689, National Bureau of Economic Research, Inc.
  3. 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.
  4. Jackson, Matthew O., 1998. "The Evolution of Social and Economic Networks," Working Papers 1044, California Institute of Technology, Division of the Humanities and Social Sciences.
  5. Bettina Klaus & Flip Klijn, 2015. "Median Stable Matching for College Admission," Working Papers 165, Barcelona Graduate School of Economics.
  6. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
  7. Roth, Alvin E & Sotomayor, Marilda, 1989. "The College Admissions Problem Revisited," Econometrica, Econometric Society, vol. 57(3), pages 559-70, May.
  8. Diamantoudi, Effrosyni & Miyagawa, Eiichi & Xue, Licun, 2004. "Random paths to stability in the roommate problem," Games and Economic Behavior, Elsevier, vol. 48(1), pages 18-28, July.
  9. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
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