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Smith and Rawls Share a Room: Stability and Medians

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  • Bettina Klaus

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

  • Flip Klijn

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

Abstract

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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Bibliographic Info

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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Keywords: fairness; matching; median; stability.;

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References

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  1. 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, Elsevier, vol. 91(1), pages 91-105, March.
  2. Bettina Klaus & Flip Klijn, 2006. "Median Stable Matching for College Admissions," International Journal of Game Theory, Springer, Springer, vol. 34(1), pages 1-11, April.
  3. 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, University of Chicago Press, vol. 92(6), pages 991-1016, December.
  4. Jackson, Matthew O. & Watts, Alison, 2002. "The Evolution of Social and Economic Networks," Journal of Economic Theory, Elsevier, Elsevier, vol. 106(2), pages 265-295, October.
  5. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, Elsevier, vol. 33(2), pages 206-230, November.
  6. Roth, Alvin E & Sotomayor, Marilda, 1989. "The College Admissions Problem Revisited," Econometrica, Econometric Society, Econometric Society, vol. 57(3), pages 559-70, May.
  7. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, Elsevier, vol. 36(2), pages 277-288, August.
  8. Diamantoudi, Effrosyni & Miyagawa, Eiichi & Xue, Licun, 2004. "Random paths to stability in the roommate problem," Games and Economic Behavior, Elsevier, Elsevier, vol. 48(1), pages 18-28, July.
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Citations

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Cited by:
  1. Florian M. Biermann, 2011. "A Measure to Compare Matchings in Marriage Markets," Working Papers, Fondazione Eni Enrico Mattei 2011.41, Fondazione Eni Enrico Mattei.
  2. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Stochastic stability for roommate markets," Journal of Economic Theory, Elsevier, Elsevier, vol. 145(6), pages 2218-2240, November.
  3. Schwarz, Michael & Yenmez, M. Bumin, 2011. "Median stable matching for markets with wages," Journal of Economic Theory, Elsevier, Elsevier, vol. 146(2), pages 619-637, March.
  4. Burak Can & Bettina Klaus, 2010. "Consistency and Population Sensitivity Properties in Marriage and Roommate Markets," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP), Université de Lausanne, Faculté des HEC, DEEP 10.08, Université de Lausanne, Faculté des HEC, DEEP.
  5. Pierre-André Chiappori & Alfred Galichon & Bernard Salanié, 2014. "The Roommate Problem - Is More Stable Than You Think," CESifo Working Paper Series 4676, CESifo Group Munich.
  6. James Boudreau & Vicki Knoblauch, 2013. "Preferences and the price of stability in matching markets," Theory and Decision, Springer, Springer, vol. 74(4), pages 565-589, April.
  7. Jens Gudmundsson, 2014. "When do stable roommate matchings exist? A review," Review of Economic Design, Springer, Springer, vol. 18(2), pages 151-161, June.
  8. Boudreau, James W. & Knoblauch, Vicki, 2014. "What price stability? Social welfare in matching markets," Mathematical Social Sciences, Elsevier, Elsevier, vol. 67(C), pages 27-33.
  9. Gudmundsson, Jens, 2011. "On symmetry in the formation of stable partnerships," Working Papers, Lund University, Department of Economics 2011:29, Lund University, Department of Economics.

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