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Credible Group Stability in Multi-Partner Matching Problems

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Author Info
Hideo Konishi
Utku Unver

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Abstract

It is known that in two-sided many-to-many matching markets, pairwise 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 define 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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Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 32.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nasm04:32

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Related research
Keywords: multipartner matching problem; pairwise stability; graph; credible deviations; responsiveness; substitutability;

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Find related papers by JEL classification:
C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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  3. John W. Hatfield & Paul Milgrom, 2005. "Auctions, Matching and the Law of Aggregate Demand," Levine's Bibliography 122247000000000780, UCLA Department of Economics. [Downloadable!]
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  7. 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)
  8. Bhaskar Dutta & Suresh Mutuswami, 1997. "Stable Networks," Tinbergen Institute Discussion Papers 97-039/1, Tinbergen Institute.
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  9. Echenique, Federico & Oviedo, Jorge, 2003. "A Theory of Stability in Many-to-Many Matching Markets," Working Papers 1185, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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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. [Downloadable!] (restricted)
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  12. Ray, Debraj, 1989. "Credible Coalitions and the Core," International Journal of Game Theory, Springer, vol. 18(2), pages 185-87.
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  14. Stef Tijs & Anne van den Nouweland & Bhaskar Dutta, 1998. "Link formation in cooperative situations," International Journal of Game Theory, Springer, vol. 27(2), pages 245-256. [Downloadable!] (restricted)
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  15. Tayfun Sönmez & Tarik Kara, 1997. "Implementation of college admission rules (*)," Economic Theory, Springer, vol. 9(2), pages 197-218.
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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. Chantarat, Sommarat & Barrett, Christopher B., 2007. "Social Network Capital, Economic Mobility and Poverty Traps," MPRA Paper 1947, University Library of Munich, Germany. [Downloadable!]
    Other versions:
  2. Echenique, Federico & Oviedo, Jorge, 2003. "A Theory of Stability in Many-to-Many Matching Markets," Working Papers 1185, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
    Other versions:
  3. Gilles, R.P. & Chakrabarti, S. & Sarangi, S. & Badasyan, N., 2004. "The role of middlemen in efficient and strongly pairwise stable networks," Discussion Paper 64, Tilburg University, Center for Economic Research. [Downloadable!]
  4. Matthew O. Jackson, 2003. "A survey of models of network formation: Stability and efficiency," Working Papers 1161, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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