The outcome of the restabilization process in matching markets

Abstract

For a many-to-one matching model, we study the matchings obtained through the restabilization of stable matchings that had been disrupted by a change in the population. We include a simple representation of the stable matching obtained in terms of the initial stable matching (i.e., before being disrupted by changes in the population) and the firm-optimal stable matching. (We used Lattice Theory to characterize the outcome of the restabilization process.) We also describe the connection between the original stable matching and the one obtained after the restabilization process in the new market.