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Stable and meta-stable contract networks

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  • Danilov, Vladimir I.
  • Karzanov, Alexander V.

Abstract

This paper studies a multilateral matching market in which each participant can sign contracts with any other agents. This market subsumes the two-sided matching and the roommate problem as special cases. We consider a hypergraph (I,C), with possible multiple (hyper)edges and loops, in which the vertices i∈I are interpreted as agents, and the edges c∈C as contracts that can be concluded between agents. The preferences of each agent i are given by a choice functionfi possessing the so-called path independent property. In this general setup we consider the notion of stable contract network.

Suggested Citation

  • Danilov, Vladimir I. & Karzanov, Alexander V., 2023. "Stable and meta-stable contract networks," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    • Handle: RePEc:eee:mateco:v:108:y:2023:i:c:s0304406823000812
    DOI: 10.1016/j.jmateco.2023.102888
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    References listed on IDEAS

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    1. Alkan, Ahmet & Gale, David, 2003. "Stable schedule matching under revealed preference," Journal of Economic Theory, Elsevier, vol. 112(2), pages 289-306, October.
    2. Charles Blair, 1988. "The Lattice Structure of the Set of Stable Matchings with Multiple Partners," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 619-628, November.
    3. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    4. Tamás Fleiner, 2003. "A Fixed-Point Approach to Stable Matchings and Some Applications," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 103-126, February.
    5. Hatfield, John William & Kominers, Scott Duke, 2017. "Contract design and stability in many-to-many matching," Games and Economic Behavior, Elsevier, vol. 101(C), pages 78-97.
    6. Marzena Rostek & Nathan Yoder, 2020. "Matching With Complementary Contracts," Econometrica, Econometric Society, vol. 88(5), pages 1793-1827, September.
    7. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    8. Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-1091, November.
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    Cited by:

    1. Chao Huang, 2023. "Multilateral matching with scale economies," Papers 2310.19479, arXiv.org.
    2. Vladimir I. Danilov, 2024. "Sequential choice functions and stability problems," Papers 2401.00748, arXiv.org, revised Mar 2024.

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    More about this item

    Keywords

    Plott choice functions; Aizerman–Malishevski theorem; Stable marriage; Hypergraph; Roommate problem; Scarf lemma;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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