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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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  1. Diamantoudi, Effrosyni & Miyagawa, Eiichi & Xue, Licun, 2004. "Random paths to stability in the roommate problem," Games and Economic Behavior, Elsevier, Elsevier, vol. 48(1), pages 18-28, July.
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  3. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, Elsevier, vol. 42(1), pages 1-12, June.
  4. John W. Hatfield & Paul Milgrom, 2005. "Auctions, Matching and the Law of Aggregate Demand," Levine's Bibliography 122247000000000780, UCLA Department of Economics.
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  6. Bettina Klaus & Flip Klijn, 2004. "Paths to Stability for Matching Markets with Couples," Working Papers 156, Barcelona Graduate School of Economics.
  7. Echenique, Federico & Oviedo, Jorge, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, Econometric Society, vol. 1(2), pages 233-273, June.
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  10. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, Elsevier, vol. 33(2), pages 206-230, November.
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  12. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, Econometric Society, vol. 50(6), pages 1483-1504, November.
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  14. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, Econometric Society, vol. 52(1), pages 47-57, January.
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  16. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 92(6), pages 991-1016, December.
  17. Tayfun Sönmez & Tarik Kara, 1997. "Implementation of college admission rules (*)," Economic Theory, Springer, Springer, vol. 9(2), pages 197-218.
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Cited by:
  1. Chantarat, Sommarat & Barrett, Christopher B., 2007. "Social Network Capital, Economic Mobility and Poverty Traps," MPRA Paper 1947, University Library of Munich, Germany.
  2. Echenique, Federico & Oviedo, Jorge, 2003. "A Theory of Stability in Many-to-Many Matching Markets," Working Papers, California Institute of Technology, Division of the Humanities and Social Sciences 1185, California Institute of Technology, Division of the Humanities and Social Sciences.
  3. Gilles, R.P. & Chakrabarti, S. & Sarangi, S. & Badasyan, N., 2004. "The Role of Middlemen inEfficient and Strongly Pairwise Stable Networks," Discussion Paper, Tilburg University, Center for Economic Research 2004-64, Tilburg University, Center for Economic Research.

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