The lattice of worker-quasi-stable matchings

Abstract: In a many-to-one matching model in which firms' preferences satisfy substitutability, we study the set of worker-quasi-stable matchings. Worker-quasi-stability is a relaxation of stability that allows blocking pairs involving a firm and an unemployed worker. We show that this set has a lattice structure and define a Tarski operator on this lattice that models a re-equilibration process and has the set of stable matchings as its fixed points.