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Absorbing sets in roommate problems

  • Iñarra, E.
  • Larrea, C.
  • Molis, E.

We analyze absorbing sets as a solution for roommate problems with strict preferences. This solution provides the set of stable matchings when it is non-empty and some matchings with interesting properties otherwise. In particular, all matchings in an absorbing set have the greatest number of agents with no incentive to change partners. These “satisfied” agents are paired in the same stable manner. In the case of multiple absorbing sets we find that any two such sets differ only in how satisfied agents are matched with each other.

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File URL: http://www.sciencedirect.com/science/article/pii/S0899825613000730
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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 81 (2013)
Issue (Month): C ()
Pages: 165-178

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Handle: RePEc:eee:gamebe:v:81:y:2013:i:c:p:165-178
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Effrosyni Diamantoudi & Eiichi Miyagawa & Licun Xue, 2002. "Random paths to stability in the roommate problem," Discussion Papers 0102-65, Columbia University, Department of Economics.
  2. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
  3. E. Inarra & C. Larrea & E. Molis, 2008. "Random paths to P-stability in the roommate problem," International Journal of Game Theory, Springer, vol. 36(3), pages 461-471, March.
  4. Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
  5. 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.
  6. Bettina Klaus & Flip Klijn & Markus Walzl, 2008. "Stochastic Stability for Roommate Markets," Working Papers 357, Barcelona Graduate School of Economics.
  7. E. Kalai & D. Schmeidler, 1975. "An Admissible Set Occurring in Various Bargaining Situations," Discussion Papers 191, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. 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.
  9. Péter Biró & Katarína Cechlárová & Tamás Fleiner, 2008. "The dynamics of stable matchings and half-matchings for the stable marriage and roommates problems," International Journal of Game Theory, Springer, vol. 36(3), pages 333-352, March.
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