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Paths to Stability for Matching Markets with Couples

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Listed author(s):
  • Bettina Klaus
  • Flip Klijn

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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File URL: http://www.barcelonagse.eu/sites/default/files/working_paper_pdfs/156.pdf
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Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 156.

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Date of creation: Oct 2004
Handle: RePEc:bge:wpaper:156
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Keywords: Matching; couples; stability; Random Paths; responsiveness;

Other versions of this item:

Find related papers by JEL classification:
  • 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
  • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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  1. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-1480, November.
  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. Bettina Klaus & Flip Klijn & Jordi Massó, 2007. "Some things couples always wanted to know about stable matchings (but were afraid to ask)," Review of Economic Design, Springer;Society for Economic Design, vol. 11(3), pages 175-184, November.
  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. 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. Ma, Jinpeng, 1996. "On Randomized Matching Mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 377-381, August.
  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. 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.
  9. Bettina Klaus & Flip Klijn & Toshifumi Nakamura, 2005. "Corrigendum: Stable Matchings and Preferences of Couples," Working Papers 261, Barcelona Graduate School of Economics.
  10. 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.
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