Binary operations and lattice structure for a model of matching with contracts

: When a set is proved to have a lattice structure, the existence within the set of one least upper bound and one greatest lower bound for each pair of its elements, relative to certain partial ordering, is showed. However, how to calculate such bounds for any pair of elements, is an additional question whose answer is not always trivial. In this paper, we address that issue for the set of stable allocations in the Many-to-one Matching with Contracts model with all the agents’preferences satisfying Substitutability and Law of Aggregated Demand (LAD). This enable us to fully describe its structure. In fact, we show that both natural operations of taking the choice set of all doctors and the choice set of all hospitals, respectively, from the union of two stable allocations, together with the unanimous-for-doctors partial ordering endow the set of stable allocations with a lattice structure. Moreover, we prove that the mentioned operations together with Blair’s partial ordering for h...

• Type: Journal
• Year: 2015
• Where: MSS
• Authors: Eliana Pepa Risma
• Keywords: Hardware, MSS 2015