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Credible Group Stability in Many-to-Many Matching Problems

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  • Hideo Konishi

    (Boston College)

  • M. Utku Ünver

    (Koç 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 EconWPA in its series Game Theory and Information with number 0309005.

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Date of creation: 06 Sep 2003
Date of revision: 06 Sep 2003
Handle: RePEc:wpa:wuwpga:0309005

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Cited by:
  1. Edward Cartwright & Myrna Wooders, 2008. "Behavioral Properties of Correlated Equilibrium; Social Group Structures with Conformity and Stereotyping," Vanderbilt University Department of Economics Working Papers 0814, Vanderbilt University Department of Economics.
  2. 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.
  3. 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.
  4. Paula Jaramillo & Çaǧatay Kayı & Flip Klijn, 2014. "On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets," Social Choice and Welfare, Springer, vol. 42(4), pages 793-811, April.
  5. Hatfield, John William & Kominers, Scott Duke, 2010. "Matching Networks with Bilateral Contracts," Research Papers 2050, Stanford University, Graduate School of Business.
  6. Bando, Keisuke, 2012. "Many-to-one matching markets with externalities among firms," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 14-20.
  7. M.Utku Unver & Fuhito Kojima, 2006. "Random Paths to Pairwise Stability in Many-to-Many Matching Problems: A Study on Market Equilibration," Working Papers 256, University of Pittsburgh, Department of Economics, revised Jan 2006.
  8. N. Roketskiy, 2012. "Farsightedly Stable Matchings," Working Papers 12-26, NET Institute.
  9. Westkamp, Alexander, 2010. "Market structure and matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1724-1738, September.
  10. Robin S. Lee & Michael Schwarz, 2009. "Interviewing in Two-Sided Matching Markets," NBER Working Papers 14922, National Bureau of Economic Research, Inc.
  11. 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.
  12. Dimitrov, Dinko & Lazarova, Emiliya, 2011. "Two-sided coalitional matchings," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 46-54, July.

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