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 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.

Item Type: | MPRA Paper |
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Original Title: | Stable and metastable contract networks |

English Title: | Stable and metastable contract networks |

Language: | English |

Keywords: | Plott choice functions, Aizerman-Malishevski 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 Decision-Making > 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.uni-muenchen.de/id/eprint/115482 |