Two-sided matching with indifferences

We allow ties in preference rankings and show that the Pareto dominance relation on stable matchings can be captured by two simple operations which involve rematching of workers and firms via cycles or chains. Likewise, the Pareto relation defined via workers' welfare can also be broken down to two similar procedures which preserve stability. Using these structural results we design fast algorithms to compute a Pareto efficient and stable matching, and a worker-optimal stable matching.