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A Measure to compare Matchings in Marriage Markets

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  • Florian M. Biermann

Abstract

In matching markets the number of blocking pairs is often used as a criterion to compare matchings. We argue that this criterion is lacking an economic interpretation: In many circumstances it will neither reflect the expected extent of partner changes, nor will it capture the satisfaction of the players with the matching. As an alternative, we set up two principles which single out a particularly "disruptive" subcollection of blocking pairs. We propose to take the cardinality of that subset as a measure to compare matchings. This cardinality has an economic interpretation: The subset is a justified objection against the given matching according to a bargaining set characterization of the set of stable matchings. We prove multiple properties relevant for a workable measure of comparison. Keywords: Stable marriage problem, Matching, Blocking pair, Instability, Matching comparison, Decentralized market, Bargaining set

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Bibliographic Info

Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp575.

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Length: 30 pages
Date of creation: Jun 2011
Date of revision:
Handle: RePEc:huj:dispap:dp575

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  1. Klijn, F. & Masso, J., 1999. "Weak Stability and a Bargaining Set for the Marriage Model," Discussion Paper 1999-114, Tilburg University, Center for Economic Research.
  2. Muriel Niederle & Alvin E Roth, 2003. "Unraveling Reduces Mobility in a Labor Market: Gastroenterology with and without a Centralized Match," Levine's Working Paper Archive 506439000000000428, David K. Levine.
  3. Kimmo Eriksson & Olle Häggström, 2008. "Instability of matchings in decentralized markets with various preference structures," International Journal of Game Theory, Springer, vol. 36(3), pages 409-420, March.
  4. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
  5. EHLERS, Lars, 2005. "Von Neumann-Morgenstern Stable Sets in Matching Problems," Cahiers de recherche 12-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  6. Bettina-Elisabeth Klaus & Flip Klijn & Markus Walzl, 2009. "Farsighted Stability for Roommate Markets," Harvard Business School Working Papers 09-135, Harvard Business School.
  7. Klaus, Bettina & Klijn, Flip, 2008. "Smith and Rawls Share a Room: Stability and Medians," Research Memoranda 009, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
  8. 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.
  9. Roth, Alvin E & Xing, Xiaolin, 1997. "Turnaround Time and Bottlenecks in Market Clearing: Decentralized Matching in the Market for Clinical Psychologists," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 284-329, April.
  10. 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.
  11. 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.
  12. Zhou Lin, 1994. "A New Bargaining Set of an N-Person Game and Endogenous Coalition Formation," Games and Economic Behavior, Elsevier, vol. 6(3), pages 512-526, May.
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Cited by:
  1. Peter Biro & Flip Klijn, 2011. "Matching with Couples: a Multidisciplinary Survey," IEHAS Discussion Papers 1139, Institute of Economics, Hungarian Academy of Sciences.

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