The lattice of worker-quasi-stable matchings
Agustin G. Bonifacio, Nadia Guinazu, Noelia Juarez, Pablo Neme and, Jorge Oviedo
TL;DR
This paper explores the structure of worker-quasi-stable matchings in a many-to-one matching model, revealing a lattice structure and a re-equilibration process that connects to stable matchings.
Contribution
It introduces the concept of worker-quasi-stability, proves the lattice structure of these matchings, and defines a Tarski operator modeling re-equilibration.
Findings
The set of worker-quasi-stable matchings forms a lattice.
A Tarski operator on this lattice models re-equilibration.
Stable matchings are fixed points of the Tarski operator.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.