Smith and Rawls Share a Room: Stability and Medians
AbstractWe 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 “lonely 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 009.
Date of creation: 2008
Date of revision:
Contact details of provider:
Web page: http://www.maastrichtuniversity.nl/web/UMPublications.htm
Economics (Jel: A);
Other versions of this item:
- Bettina Klaus & Flip Klijn, 2010. "Smith and Rawls share a room: stability and medians," Social Choice and Welfare, Springer, vol. 35(4), pages 647-667, October.
- Bettina Klaus & Flip Klijn, 2009. "Smith and Rawls Share a Room: Stability and Medians," Harvard Business School Working Papers 09-111, Harvard Business School.
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-05-24 (All new papers)
- NEP-CDM-2008-05-24 (Collective Decision-Making)
- NEP-GTH-2008-05-24 (Game Theory)
- NEP-HPE-2008-05-24 (History & Philosophy of Economics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Roth, Alvin E, 1986. "On the Allocation of Residents to Rural Hospitals: A General Property of Two-Sided Matching Markets," Econometrica, Econometric Society, vol. 54(2), pages 425-27, March.
- Michael Schwarz & M. Bumin Yenmez, 2009. "Median Stable Matching," NBER Working Papers 14689, National Bureau of Economic Research, Inc.
- 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.
- Jackson, Matthew O. & Watts, Alison, 2002.
"The Evolution of Social and Economic Networks,"
Journal of Economic Theory,
Elsevier, vol. 106(2), pages 265-295, October.
- 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.
- Roth, Alvin E. & Sotomayor, Marilda, 1992.
Handbook of Game Theory with Economic Applications,
in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541
- Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
- Bettina Klaus & Flip Klijn, 2004.
"Median Stable Matching for College Admission,"
165, Barcelona Graduate School of Economics.
- Klaus, Bettina & Klijn, Flip, 2006. "Median stable matching for college admissions," Open Access publications from Maastricht University urn:nbn:nl:ui:27-20032, Maastricht University.
- Bettina Klaus & Flip Klijn, 2004. "Median Stable Matching for College Admission," UFAE and IAE Working Papers 632.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 16 Feb 2006.
- Roth, Alvin E & Sotomayor, Marilda, 1989. "The College Admissions Problem Revisited," Econometrica, Econometric Society, vol. 57(3), pages 559-70, May.
- 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.
- 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.
- Florian M. Biermann, 2011.
"A Measure to compare Matchings in Marriage Markets,"
Discussion Paper Series
dp575, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- Florian M. Biermann, 2011. "A Measure to Compare Matchings in Marriage Markets," Working Papers 2011.41, Fondazione Eni Enrico Mattei.
- Florian M. Biermann, 2011. "A Measure to compare Matchings in Marriage Markets," Working Papers 005-11, International School of Economics at TSU, Tbilisi, Republic of Georgia.
- Bettina Klaus & Flip Klijn & Markus Walzl, 2008.
"Stochastic Stability for Roommate Markets,"
357, Barcelona Graduate School of Economics.
- Schwarz, Michael & Yenmez, M. Bumin, 2011. "Median stable matching for markets with wages," Journal of Economic Theory, Elsevier, vol. 146(2), pages 619-637, March.
- Gudmundsson, Jens, 2011. "On symmetry in the formation of stable partnerships," Working Papers 2011:29, Lund University, Department of Economics.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Charles Bollen).
If references are entirely missing, you can add them using this form.