Representing All Stable Matchings by Walking a Maximal Chain
Computer Science and Game Theory
2019-10-11 v1 Theoretical Economics
Abstract
The seminal book of Gusfield and Irving [GI89] provides a compact and algorithmically useful way to represent the collection of stable matches corresponding to a given set of preferences. In this paper, we reinterpret the main results of [GI89], giving a new proof of the characterization which is able to bypass a lot of the "theory building" of the original works. We also provide a streamlined and efficient way to compute this representation. Our proofs and algorithms emphasize the connection to well-known properties of the deferred acceptance algorithm.
Keywords
Cite
@article{arxiv.1910.04401,
title = {Representing All Stable Matchings by Walking a Maximal Chain},
author = {Linda Cai and Clayton Thomas},
journal= {arXiv preprint arXiv:1910.04401},
year = {2019}
}