Lattice operations for the stable set in substitutable matching markets via re-equilibration dynamics
<|reference_start|>Lattice operations for the stable set in substitutable matching markets via re-equilibration dynamics: We compute the lattice operations for the (pairwise) stable set in two-sided matching markets where only substitutability on agents' choice functions is imposed. To do this, we use 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. First, we compute the lattice operations in the many-to-one model. Then, we extend these operations to a many-to-many model with substitutable choice functions on one side and responsive preferences on the other, via a morphism that relates many-to-one with many-to-many matchings in a natural way. Finally, we present the lattice operations in the many-to-many model with substitutable choice functions on both sides.<|reference_end|>
@article{bonifacio2024lattice,
    title={Lattice operations for the stable set in substitutable matching markets
  via re-equilibration dynamics},
    author={Agustin G. Bonifacio and Noelia Juarez and Paola B. Manasero},
    journal={arXiv preprint arXiv:2407.21198},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.21198},
    primaryClass={econ.TH cs.GT}
}