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Paths to stability for matching markets with couples

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  • Klaus, Bettina
  • Klijn, Flip

Abstract

We study two-sided matching markets with couples and show that for a natural preference domain for couples, the domain of weakly responsive preferences, stable outcomes can always be reached by means of decentralized decision making. Starting from an arbitrary matching, we construct a path of matchings obtained from `satisfying' blocking coalitions that yields a stable matching. Hence, we establish a generalization of Roth and Vande Vate's (1990) result on path convergence to stability for decentralized singles markets. Furthermore, we show that when stable matchings exist, but preferences are not weakly responsive, for some initial matchings there may not exist any path obtained from `satisfying' blocking coalitions that yields a stable matching.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 58 (2007)
Issue (Month): 1 (January)
Pages: 154-171

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Handle: RePEc:eee:gamebe:v:58:y:2007:i:1:p:154-171

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. Bettina Klaus & Flip Klijn, 2002. "Some things couples always wanted to know about stable matchings (but were afraid to ask)," UFAE and IAE Working Papers 552.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 01 Oct 2005.
  2. 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.
  3. Klaus, Bettina & Klijn, Flip & Nakamura, Toshifumi, 2007. "Corrigendum: Stable Matchings and Preferences of Couples," Research Memorandum 025, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  4. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, vol. 121(1), pages 75-106, March.
  5. Elliott Peranson & Alvin E. Roth, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," American Economic Review, American Economic Association, vol. 89(4), pages 748-780, September.
  6. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-80, November.
  7. 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.
  8. 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.
  9. Alvin E. Roth, 2002. "The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics," Econometrica, Econometric Society, vol. 70(4), pages 1341-1378, July.
  10. Ma, Jinpeng, 1996. "On Randomized Matching Mechanisms," Economic Theory, Springer, vol. 8(2), pages 377-81, August.
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Citations

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Cited by:
  1. Bettina Klaus & Flip Klijn & Markus Walzl, 2011. "Farsighted Stability for Roommate Markets," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 13(6), pages 921-933, December.
  2. Bo Chen & Satoru Fujishige & Zaifu Yang, 2011. "Decentralized Market Processes to Stable Job Matchings with Competitive Salaries," Discussion Papers 11/03, Department of Economics, University of York.
  3. Peter Biro & Flip Klijn, 2011. "Matching with Couples: a Multidisciplinary Survey," IEHAS Discussion Papers 1139, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  4. Hideo Konishi & Utku Unver, 2004. "Credible Group Stability in Multi-Partner Matching Problems," Econometric Society 2004 North American Summer Meetings 32, Econometric Society.
  5. Bettina Klaus & Flip Klijn, 2004. "Fair and Efficient Student Placement with Couples," Working Papers 145, Barcelona Graduate School of Economics.
  6. Bettina Klaus & Frédéric Payot, 2013. "Paths to Stability in the Assignment Problem," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 13.14, Université de Lausanne, Faculté des HEC, DEEP.
  7. James Boudreau, 2008. "Preference Structure and Random Paths to Stability in Matching Markets," Economics Bulletin, AccessEcon, vol. 3(67), pages 1-12.
  8. Claus-Jochen Haake & Bettina Klaus, 2010. "Stability and Nash implementation in matching markets with couples," Theory and Decision, Springer, vol. 69(4), pages 537-554, October.
  9. Vilmos Komornik & Christelle Viauroux, 2012. "Conditional Stable Matchings," UMBC Economics Department Working Papers 12-03, UMBC Department of Economics.
  10. repec:ebl:ecbull:v:3:y:2008:i:67:p:1-12 is not listed on IDEAS
  11. Fuhito Kojima & M. Ünver, 2008. "Random paths to pairwise stability in many-to-many matching problems: a study on market equilibration," International Journal of Game Theory, Springer, vol. 36(3), pages 473-488, March.
  12. Alfredo Salgado-Torres, 2012. "A simple decentralized matching mechanism in markets with couples," Economics Bulletin, AccessEcon, vol. 32(3), pages 2044-2055.
  13. Yang, Yi-You, 2012. "On the accessibility of core-extensions," Games and Economic Behavior, Elsevier, vol. 74(2), pages 687-698.

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