Stable and metastable contract networks

Vladimir Danilov and Alexander Karzanov

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Plott choice functions; Aizerman-Malishevski theorem; stable marriage; roommate problem; Scarf lemma (search for similar items in EconPapers)
JEL-codes: C71 C78 D74 (search for similar items in EconPapers)
Date: 2022-11-29
New Economics Papers: this item is included in nep-cta, nep-des, nep-net and nep-upt
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Related works:
Journal Article: Stable and meta-stable contract networks (2023)
Working Paper: Stable and metastable contract networks (2023)
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:115482

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