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Credible Group Stability in Multi-Partner Matching Problems

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  • Hideo Konishi

    (Department of Economics, Boston College)

  • M. Utku Ünver

    (Department of Economics, Koç University)

Abstract

It is known that in two-sided many-to-many matching markets, pair-wise stability is not logically related with the (weak) core, unlike in many-to-one matching markets (Blair, 1988). In this paper, we seek a theoretical foundation for pairwise stability when group deviations are allowed. Group deviations are defined in graphs on the set of agents. We introduce executable group deviations in order to discuss the credibility of group deviations and to defined credibly group stable matchings. We show, under responsive preferences, that credible group stability is equivalent to pairwise stability in the multi-partner matching problem that includes two-sided matching problems as special cases. 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. However, under a weaker preference restriction, substitutability, these equivalences no longer hold, since pairwise stable matchings may be strictly Pareto-ordered, unlike under responsiveness.

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Bibliographic Info

Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2003.115.

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Date of creation: Dec 2003
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Handle: RePEc:fem:femwpa:2003.115

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Keywords: Multi-partner matching problem; Pairwise stable matching network; Credible group deviation;

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References

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  1. Dutta, B. & Nouweland, C.G.A.M. van den & Tijs, S.H., 2003. "Link formation in cooperative situations," Open Access publications from Tilburg University urn:nbn:nl:ui:12-121826, Tilburg University.
  2. Klaus, Bettina & Klijn, Flip, 2007. "Paths to stability for matching markets with couples," Games and Economic Behavior, Elsevier, vol. 58(1), pages 154-171, January.
  3. Echenique, Federico, 2007. "Counting combinatorial choice rules," Games and Economic Behavior, Elsevier, vol. 58(2), pages 231-245, February.
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  7. Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2000. "Single Agents and the Set of Many-to-One Stable Matchings," Journal of Economic Theory, Elsevier, vol. 91(1), pages 91-105, March.
  8. 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.
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  10. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
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  13. 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.
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  17. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
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Citations

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Cited by:
  1. Federico Echenique & Jorge Oviedo, 2003. "A Theory of Stability in Many-to-many Matching Markets," Levine's Working Paper Archive 666156000000000374, David K. Levine.
  2. Chantarat, Sommarat & Barrett, Christopher B., 2008. "Social Network Capital, Economic Mobility and Poverty Traps," MPRA Paper 6841, University Library of Munich, Germany.
  3. Gilles, R.P. & Chakrabarti, S. & Sarangi, S. & Badasyan, N., 2004. "The Role of Middlemen inEfficient and Strongly Pairwise Stable Networks," Discussion Paper 2004-64, Tilburg University, Center for Economic Research.

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