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.
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
.
DOI: 10.1007/s40305-019-00246-z
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