Título: Matching with contracts: a deferred acceptance algorithm and the fullset of stable allocations
Abstract: In this paper, we present a deferred-acceptance algorithm for the model of Matching with Contracts Many-to-many with all the agents' preferences satisfying Substitutability. Therefore, we provide a constructive proof of the existence of at least one stable allocation for this model and show that it is the optimal allocation for the agents which make the offers and the worst stable allocation for the other market-side. Also, we include a proof of the fact that the set of stable allocations has lattice structure with respect to the Blair´s partial orderings for each market-side. Such lattices are dual, so there is a counterposition of interests between both market-sides. Finally, we use our deferred-acceptance algorithm and the mentioned lattice structure to calculate the complete set of stable allocations.
Expositora: Dra. Eliana Pepa Risma (integrante del grupo de investigación de Teoría de Juegos del IMASL).