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

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  • Hideo Konishi

    ()
    (Boston College)

  • M. Utku Unver

    (Koc University)

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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Bibliographic 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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Keywords: social welfare; GATT think; quasi-linear utility;

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References

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Citations

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Cited by:
  1. Paula Jaramillo & Cagatay Kay & Flip Klijn, 2012. "On the Exhaustiveness of Truncation and Dropping Strategies in Many-to-Many Matching Markets," DOCUMENTOS CEDE 010316, UNIVERSIDAD DE LOS ANDES-CEDE.
  2. 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.
  3. Klaus, Bettina & Walzl, Markus, 2006. "Stable Many-to-Many Matchings with Contracts," Research Memorandum 042, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  4. Dimitrov, Dinko & Lazarova, Emiliya, 2011. "Two-sided coalitional matchings," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 46-54, July.
  5. Hatfield, John William & Kojima, Fuhito, 2010. "Substitutes and stability for matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1704-1723, September.
  6. Westkamp, Alexander, 2010. "Market structure and matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1724-1738, September.
  7. Bando, Keisuke, 2012. "Many-to-one matching markets with externalities among firms," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 14-20.
  8. Robin S. Lee & Michael Schwarz, 2009. "Interviewing in Two-Sided Matching Markets," NBER Working Papers 14922, National Bureau of Economic Research, Inc.
  9. Hatfield, John William & Kominers, Scott Duke, 2010. "Matching Networks with Bilateral Contracts," Research Papers 2050, Stanford University, Graduate School of Business.

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