Lattice operations for the stable set in many-to-many markets via re-equilibration dynamics

We compute the lattice operations for the (pairwise) stable set in many-to-many matching markets where only path-independence on agents' choice functions is imposed. To do this, we construct Tarski operators defined on the lattices of worker-quasi-stable and firm-quasi-stable matchings. These operators resemble lay-off and vacancy chain dynamics, respectively.