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Stable and metastable contract networks

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  • Danilov, Vladimir
  • Karzanov, Alexander

Abstract

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 concerning the contracts where i takes part are given by use of a choice function fi possessing the so-called path independent property. In this general setup we introduce the notion of stable network of contracts. The paper contains two main results. The first one is that a general problem on stable systems of contracts for (I, C, f) is reduced to a set of special ones in which preferences of agents are described by use of so-called weak orders, or utility functions. However, for a special case of this sort, the stability may not exist. Trying to overcome this trouble when dealing with such special cases, we introduce a weaker notion of metastability for systems of contracts. Our second result is that a metastable system always exists.

Suggested Citation

  • Danilov, Vladimir & Karzanov, Alexander, 2022. "Stable and metastable contract networks," MPRA Paper 115482, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:115482
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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. 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.
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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; 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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