This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

Smith and Rawls Share a Room: Stability and Medians

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
Bettina Klaus () (Harvard Business School, Negotiation, Organizations & Markets Unit)
Flip Klijn () (Institute for Economic Analysis (CSIC), Campus UAB, Barcelona, Spain)

Additional information is available for the following registered author(s):

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.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. 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.

File URL: http://www.hbs.edu/research/pdf/09-111.pdf
File Format: application/pdf
File Function:
Download Restriction: no

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

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 23 pages
Date of creation: Feb 2009
Date of revision:
Handle: RePEc:hbs:wpaper:09-111

Contact details of provider:
Postal: Soldiers Field, Boston, Massachusetts 02163
Phone: 617.495.6000
Web page: http://www.hbs.edu/
More information through EDIRC

For technical questions regarding this item, or to correct its listing, contact: (Soebagio Notosoehardjo).

Related research
Keywords: fairness; matching; median; stability.;

Other versions of this item:

Find related papers by JEL classification:
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - 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:

References listed on IDEAS
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.:
  1. 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. [Downloadable!] (restricted)
  2. Roth, Alvin E & Sotomayor, Marilda, 1989. "The College Admissions Problem Revisited," Econometrica, Econometric Society, vol. 57(3), pages 559-70, May. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
    Other versions:
  4. 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. [Downloadable!] (restricted)
    Other versions:
  5. Bettina Klaus & Flip Klijn, 2006. "Median Stable Matching for College Admissions," International Journal of Game Theory, Springer, vol. 34(1), pages 1-11, April. [Downloadable!] (restricted)
    Other versions:
  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. [Downloadable!] (restricted)
  7. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," 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 Elsevier. [Downloadable!] (restricted)
  8. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, 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.)

  1. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2008. "Stochastic Stability for Roommate Markets," Research Memoranda 010, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
Statistics
Access and download statistics

Did you know? IDEAS also indexes books.

This page was last updated on 2009-11-19.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.