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

DRA. PAOLA B. MANASERO

Buenos Aires

Encuentro; ANNUAL MEETING OF THE LATIN AMERICAN AND CARIBBEAN ECONOMIC ASSOCIATION AND LATIN AMERICAN MEETING OF THE ECONOMETRIC SOCIETY; 2017

Universidad de San Andrés

We study a many-to-many matching problem with the restriction of substitutability and law of aggregate demand (LAD) for all preferences for one side of the market, the firms, and responsive preferences to the other side, the workers. We define two binary operations to compute the least upper bound (l.u.b.) and the greatest lower bound (g.l.b.) for each pair of stable matchings concerning the Blair's partial ordering for the agents. By using these operations, we give an alternative proof that the set of stable matchings has a lattice structures. The main contribution of this paper is that we give a mechanism for obtaining two binary operations in a many-to-many matching problem. In addition, other contribution of this paper is that both binary operations are obtained as an extension of a many-to-one matching problem.