 Canonical Monotone Decompositions of Fractional Stable MatchingsHernan G Abeledo, Yosef Blum and Uriel G Rothblum International Journal of Game Theory, 1996, vol. 25, issue 2, 76 pages Abstract: The paper continues recent work that introduced algebraic methods for studying the stable marriage problem of Gale and Shapley (1962). Vande Vate (1989) and Rothblum (1992) identified a set of linear inequalities which define a polytope whose extreme points correspond to the stable matchings. Points in the polytope are called fractional stable matchings. Here we identify a unique representation of fractional stable matchings as a convex combination of stable matchings that are arrangeable in a man-decreasing order. We refer to this representation and to a dual one, in terms of woman-decreasing order, as the canonical monotone representations. These representations can be interpreted as time-sharing stable matchings where particular stable matchings are used at each time-instance but the scheduled stable matchings are (occasionally) switched over time. The new representations allow us to extend, in a natural way, the lattice structure of the set of stable matchings to the set of all fractional stable matchings. Date: 1996 There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:jogath:v:25:y:1996:i:2:p:161-76 Ordering information: This journal article can be ordered from Access Statistics for this article International Journal of Game Theory is currently edited by Shmuel Zamir, Vijay Krishna and Bernhard von Stengel More articles in International Journal of Game Theory from Springer, Game Theory Society |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.