The outcome of the restabilization process in matching markets

TL;DR

This paper analyzes how stable matchings in many-to-one markets are affected by population changes, using lattice theory to characterize the restabilization outcomes and their relation to initial matchings.

Contribution

It introduces a lattice-theoretic framework to describe the restabilization process after market disruptions due to population changes.

Findings

Characterizes restabilized matchings using lattice theory.

Connects original and post-disruption stable matchings.

Provides a simple representation of the restabilization outcome.

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.