Lattice Structure of Many-to-one Stable Matchings

LI Jianrong

Acta Mathematicae Applicatae Sinica ›› 2015, Vol. 38 ›› Issue (4) : 641-649.

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PDF(339 KB)
Acta Mathematicae Applicatae Sinica ›› 2015, Vol. 38 ›› Issue (4) : 641-649. DOI: 10.12387/C2015060

Lattice Structure of Many-to-one Stable Matchings

  • LI Jianrong
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Abstract

The game-theoretic solutions defined in two-sided market allow the interests of agents on the same side of the market to be simultaneously maximized. The theoretic basis of such kind of optimization is the stability of the selection matchings, the stability of the selection matchings endows the set of stable matchings a lattice structure, and the lattice structure of the stable matchings give paths to the optimal outcomes. This paper uses game-theoretic method to study the optimal-path in many-to-one two-sided matching market, we prove that the set of stable matchings is a complete distributive lattice under Blair's partial order.

Key words

matching game / stabile matching / lattice

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LI Jianrong. Lattice Structure of Many-to-one Stable Matchings. Acta Mathematicae Applicatae Sinica, 2015, 38(4): 641-649 https://doi.org/10.12387/C2015060

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