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Market structure and matching with contracts

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  • Westkamp, Alexander
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    Abstract

    Ostrovsky (2008) [9] develops a theory of stability for a model of matching in exogenously given networks. For this model a generalization of pairwise stability, chain stability, can always be satisfied as long as agents' preferences satisfy same side substitutability and cross side complementarity. Given this preference domain I analyze the interplay between properties of the network structure and (cooperative) solution concepts. The main structural condition is an acyclicity notion that rules out the implementation of trading cycles. It is shown that this condition and the restriction that no pair of agents can sign more than one contract with each other are jointly necessary and sufficient for (i) the equivalence of group and chain stability, (ii) the core stability of chain stable networks, (iii) the efficiency of chain stable networks, (iv) the existence of a group stable network, and (v) the existence of an efficient and individually stable network. These equivalences also provide a rationale for chain stability in the unrestricted model. The (more restrictive) conditions under which chain stability coincides with the core are also characterized.

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    Bibliographic Info

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

    Volume (Year): 145 (2010)
    Issue (Month): 5 (September)
    Pages: 1724-1738

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    Handle: RePEc:eee:jetheo:v:145:y:2010:i:5:p:1724-1738

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

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    Keywords: Matching with contracts Network structure Chain stability Acyclicity Group stability Core Efficiency;

    References

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    1. 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.
    2. Matthew O. Jackson & Asher Wolinsky, 1994. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Konishi, Hideo & Unver, M. Utku, 2006. "Credible group stability in many-to-many matching problems," Journal of Economic Theory, Elsevier, vol. 129(1), pages 57-80, July.
    4. Ning Sun & Zaifu Yang, 2006. "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, Econometric Society, vol. 74(5), pages 1385-1402, 09.
    5. Roth, Alvin, 2008. "Deferred Acceptance Algorithms: History, Theory, Practice, and Open Questions," Scholarly Articles 2579651, Harvard University Department of Economics.
    6. Jorge Oviedo & Federico Echenique, 2005. "A Theory of Stability in Many-to-Many Matching Markets," 2005 Meeting Papers 233, Society for Economic Dynamics.
    7. 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.
    8. Kalai, Ehud & Postlewaite, Andrew & Roberts, John, 1978. "Barriers to trade and disadvantageous middlemen: Nonmonotonicity of the core," Journal of Economic Theory, Elsevier, vol. 19(1), pages 200-209, October.
    9. Michael Ostrovsky, 2008. "Stability in Supply Chain Networks," American Economic Review, American Economic Association, vol. 98(3), pages 897-923, June.
    10. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    11. Papai, Szilvia, 2007. "Exchange in a general market with indivisible goods," Journal of Economic Theory, Elsevier, vol. 132(1), pages 208-235, January.
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    Cited by:
    1. Tayfun Sönmez & Tobias B. Switzer, 2011. "Matching with (Branch-of-Choice) Contracts at United States Military Academy," Boston College Working Papers in Economics 782, Boston College Department of Economics.
    2. John William Hatfield & Scott Duke Kominers, 2012. "Matching in Networks with Bilateral Contracts," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 176-208, February.

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