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Credible group stability in many-to-many matching problems

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  • Konishi, Hideo
  • Unver, M. Utku

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

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 129 (2006)
Issue (Month): 1 (July)
Pages: 57-80

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Handle: RePEc:eee:jetheo:v:129:y:2006:i:1:p:57-80

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Web page: http://www.elsevier.com/locate/inca/622869

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Cited by:
  1. Paula Jaramillo & Kagi Cagatay & Flip Klijn, 2012. "On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets," DOCUMENTOS DE TRABAJO 009997, UNIVERSIDAD DEL ROSARIO.
  2. 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.
  3. Dimitrov, Dinko & Lazarova, Emiliya, 2011. "Two-sided coalitional matchings," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 46-54, July.
  4. Robin S. Lee & Michael Schwarz, 2009. "Interviewing in Two-Sided Matching Markets," NBER Working Papers 14922, National Bureau of Economic Research, Inc.
  5. Klaus, Bettina & Walzl, Markus, 2009. "Stable many-to-many matchings with contracts," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 422-434, July.
  6. Hatfield, John William & Kominers, Scott Duke, 2010. "Matching Networks with Bilateral Contracts," Research Papers 2050, Stanford University, Graduate School of Business.
  7. Westkamp, Alexander, 2010. "Market structure and matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1724-1738, September.
  8. 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.
  9. Bando, Keisuke, 2012. "Many-to-one matching markets with externalities among firms," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 14-20.

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