Binary Operations for the Lattice Structure in a Many-to-Many Matching Model

doi:10.1007/s40305-019-00246-z

Journal of the Operations Research Society of China ›› 2021, Vol. 9 ›› Issue (1): 207-228.doi: 10.1007/s40305-019-00246-z

Binary Operations for the Lattice Structure in a Many-to-Many Matching Model

Paola Belén Manasero

Instituto de Matemática Aplicada San Luis, Universidad Nacional de San Luis and CONICET, Av. Ejército de los andes 950, D5700 HHW San Luis, Argentina

Received:2018-06-05 Revised:2018-10-12 Online:2021-03-11 Published:2021-03-11
Contact: Paola Belén Manasero E-mail:pbmanasero@unsl.edu.ar
Supported by:
This research was supported by the Universidad Nacional de San Luis (No. 31012), and by the Consejo Nacional de Investigaciones Científicas y Técnicas (No. PIP 112-201501-00464).

Abstract

Abstract: The lattice structure of the set of stable matchings in many-to-many matching model is well known in literature. If preferences of the agents are substitutable, this result can be obtained by fixed-point methods, for that purpose an algorithm for finding a fixed-point matching is defined. Since the fixed-point set equals the set of stable matchings, the latter has a lattice structure too. In this paper, we consider a many-to-many matching market where the preferences of firms satisfy substitutability and the law of aggregate demand, and workers have responsive preferences. In this many-to-many matching market, we explicitly compute for any pair of stable matchings the least upper bound and the greatest lower bound, without using fixed-point methods.

Key words: Many-to-many matching model, Binary operations, Lattice structure

CLC Number:

91B68

Paola Belén Manasero. Binary Operations for the Lattice Structure in a Many-to-Many Matching Model[J]. Journal of the Operations Research Society of China, 2021, 9(1): 207-228.

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Binary Operations for the Lattice Structure in a Many-to-Many Matching Model

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