Danilov, Vladimir and Karzanov, Alexander (2022): Stable and metastable contract networks.

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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 socalled 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 socalled 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.
Item Type:  MPRA Paper 

Original Title:  Stable and metastable contract networks 
English Title:  Stable and metastable contract networks 
Language:  English 
Keywords:  Plott choice functions, AizermanMalishevski theorem, stable marriage, roommate problem, Scarf lemma 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C71  Cooperative Games C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C78  Bargaining Theory ; Matching Theory D  Microeconomics > D7  Analysis of Collective DecisionMaking > D74  Conflict ; Conflict Resolution ; Alliances ; Revolutions 
Item ID:  115482 
Depositing User:  Dmitry Ilinskiy 
Date Deposited:  29 Nov 2022 11:51 
Last Modified:  29 Nov 2022 11:52 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/115482 