Binary Operations and Lattice Structure for a Many-to-Many Matching Model

We define two binary operations to calculate the least upper bound (l.u.b.) and the greatest lower bound (g.l.b.) for each pair of stable matchings according to the Blair's partial ordering to the agents in a many-to-many... [ view full abstract ]

We define two binary operations to calculate the least upper bound (l.u.b.) and the greatest lower bound (g.l.b.) for each pair of stable matchings according to the Blair's partial ordering to the agents in a many-to-many matching model with the restriction of substitutability and law of aggregate demand (LAD) for all preferences for one side of the market, and responsive with quota preferences to the other side. Using these operations, we show that the set of stable matchings has lattice structures. These binary operations are obtain using the bijective function, φ_{S}, defined by Manasero, P. (2016), which preserve the stability of the matchings between certain many-to-many models and the related many-to-one model. In this way, both binary operations are obtain as an extension of the binary operations defined by Pepa Risma, E. (2015) in the case many-to-one matching model.