Strong core and Pareto-optimality in the multiple partners matching problem under lexicographic preference domains

We study strong core and Pareto-optimal solutions for multiple partners matching problem under lexicographic preference domains from a computational point of view. The restriction to the two-sided case is called stable many-to-many matching problem and the general one-sided case is called stable fix...

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Bibliographic Details
Published in:Games and economic behavior Vol. 145; pp. 217 - 238
Main Authors: Biró, Péter, Csáji, Gergely
Format: Journal Article
Language:English
Published: Elsevier Inc 01.05.2024
Subjects:
Computation complexity
Core
Lexicographic preferences
Many-to-many matching
Stable matchings
Computation complexity
Lexicographic preferences
Many-to-many matching
Stable matchings
Core
ISSN:0899-8256, 1090-2473
Online Access:Get full text
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Summary:We study strong core and Pareto-optimal solutions for multiple partners matching problem under lexicographic preference domains from a computational point of view. The restriction to the two-sided case is called stable many-to-many matching problem and the general one-sided case is called stable fixtures problem. We provide an example to show that the strong core can be empty even for many-to-many problems, and that deciding the non-emptiness of the strong core is NP-hard. On the positive side, we give efficient algorithms for finding a near feasible strong core solution and for finding a fractional matching in the strong core of fractional matchings. In contrast with the NP-hardness result for the stable fixtures problem, we show that finding a maximum size matching that is Pareto-optimal can be done efficiently for many-to-many problems. Finally, we show that for reverse-lexicographic preferences the strong core is always non-empty in the many-to-many case.
ISSN:0899-8256
1090-2473
DOI:10.1016/j.geb.2024.03.010