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Credible Group-Stability in Many-to-Many Matching Problems

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Author Info
Hideo Konishi () (Boston College)
M. Utku Unver (Koc University)

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Abstract

It is known that in two-sided many-to-many matching problems, pairwise-stable matchings may not be immune to group deviations, unlike in many-to-one matching problems (Blair 1988). In this paper, we show that pairwise stability is equivalent to credible group stability when one side has responsive preferences and the other side has categorywise-responsive preferences. A credibly group-stable matching is immune to any "executable" group deviations with an appropriate definition of executability. Under the same preference restriction, we also show the equivalence between the set of pairwise-stable matchings and the set of matchings generated by coalition-proof Nash equilibria of an appropriately defined strategic-form game.

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Publisher Info
Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 570.

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Length: 30 pages
Date of creation: 05 Sep 2003
Date of revision: 19 Jan 2005
Publication status: published, Journal of Economic Theory, 129, 57-80 (2006)
Handle: RePEc:boc:bocoec:570

Note: This paper was previously circulated as "Credible Group-Stability in Multi-Partner Matching Problems"
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Related research
Keywords: social welfare; GATT think; quasi-linear utility;

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
J44 - Labor and Demographic Economics - - Particular Labor Markets - - - Professional Labor Markets and Occupations

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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.:
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  3. 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)
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  4. 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)
  5. Roth, Alvin E, 1991. "A Natural Experiment in the Organization of Entry-Level Labor Markets: Regional Markets for New Physicians and Surgeons in the United Kingdom," American Economic Review, American Economic Association, vol. 81(3), pages 415-40, June. [Downloadable!] (restricted)
  6. 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)
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  8. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January. [Downloadable!] (restricted)
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  12. Tayfun Sönmez & Tarik Kara, 1997. "Implementation of college admission rules (*)," Economic Theory, Springer, vol. 9(2), pages 197-218.
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  17. 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)
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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. Bettina-Elisabeth Klaus & Markus Walzl, 2007. "Stable Many-to-Many Matchings with Contracts," Harvard Business School Working Papers 09-046, Harvard Business School, revised Sep 2008. [Downloadable!]
    Other versions:
  2. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2006. "Farsightedly Stable Networks," Research Memoranda 041, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
    Other versions:
  3. 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. [Downloadable!] (restricted)
    Other versions:
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