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Stable and metastable contract networks

Author

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  • Vladimir I. Danilov
  • Alexander V. Karzanov

Abstract

We consider a hypergraph (I,C), with possible multiple (hyper)edges and loops, in which the vertices $i\in I$ are interpreted as agents, and the edges $c\in C$ 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 $f_i$ 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

  • Vladimir I. Danilov & Alexander V. Karzanov, 2022. "Stable and metastable contract networks," Papers 2202.13089, arXiv.org, revised May 2023.
    • Handle: RePEc:arx:papers:2202.13089
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    References listed on IDEAS

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    1. 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.
    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

    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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