Counting steps for re-stabilization in a labor matching market
Theoretical Economics
2024-05-14 v1 Computer Science and Game Theory
Abstract
We study a one-to-one labor matching market. If a worker considers resigning from her current job to obtain a better one, how long does it take for this worker to actually get it? We present an algorithm that models this situation as a re-stabilization process involving a vacancy chain. Each step of the algorithm is a link of such a chain. We show that the length of this vacancy chain, which can be interpreted as the time the worker has to wait for her new job, is intimately connected with the lattice structure of the set of stable matchings of the market. Namely, this length can be computed by considering the cardinalities of cycles in preferences derived from the initial and final stable matchings involved.
Keywords
Cite
@article{arxiv.2405.07084,
title = {Counting steps for re-stabilization in a labor matching market},
author = {Agustin G. Bonifacio and Nadia Guiñazu and Noelia Juarez and Pablo Neme and Jorge Oviedo},
journal= {arXiv preprint arXiv:2405.07084},
year = {2024}
}