The cone of supermodular games on finite distributive lattices

被引：4
|
作者：
Grabisch, Michel [1 ]
Kroupa, Tomas [2 ]
机构：
[1] Univ Paris 01, Paris Sch Econ, Paris, France
[2] Czech Acad Sci, Inst Informat Theory & Automat, Prague, Czech Republic
来源：
DISCRETE APPLIED MATHEMATICS | 2019年 / 260卷
关键词：
Supermodular/submodular function; Core; Coalitional game; Polyhedral cone;
D O I：
10.1016/j.dam.2019.01.024
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article we study supermodular functions on finite distributive lattices. Relaxing the assumption that the domain is a powerset of a finite set, we focus on geometrical properties of the polyhedral cone of such functions. Specifically, we generalize the criterion for extremality and study the face lattice of the supermodular cone. An explicit description of facets by the corresponding tight linear inequalities is provided. (C) 2019 Elsevier B.V. All rights reserved.
引用
收藏
页码：144 / 154
页数：11
相关论文
共 50 条
  • [1] Supermodular programming on finite lattices
    Khachaturov, Vladimir R.
    Khachaturov, Roman V.
    Khachaturov, Ruben V.
    [J]. COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2012, 52 (06) : 855 - 878
  • [2] Supermodular Functions on Finite Lattices
    S. David Promislow
    Virginia R. Young
    [J]. Order, 2005, 22 : 389 - 413
  • [3] Supermodular programming on finite lattices
    Vladimir R. Khachaturov
    Roman V. Khachaturov
    Ruben V. Khachaturov
    [J]. Computational Mathematics and Mathematical Physics, 2012, 52 : 855 - 878
  • [4] Supermodular functions on finite lattices
    Promislow, SD
    Young, VR
    [J]. ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2005, 22 (04): : 389 - 413
  • [5] The Core of Games on Distributive Lattices
    Xie, Lijue
    Grabisch, Michel
    [J]. NEW DIMENSIONS IN FUZZY LOGIC AND RELATED TECHNOLOGIES, VOL I, PROCEEDINGS, 2007, : 313 - 317
  • [6] A CHARACTERIZATION OF FINITE DISTRIBUTIVE LATTICES
    FAIGLE, U
    [J]. REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES, 1981, 26 (02): : 211 - 212
  • [7] PARENTHESIZATIONS OF FINITE DISTRIBUTIVE LATTICES
    GANSNER, ER
    [J]. ALGEBRA UNIVERSALIS, 1983, 16 (03) : 287 - 303
  • [8] FINITE PROJECTIVE DISTRIBUTIVE LATTICES
    GRATZER, G
    WOLK, B
    [J]. CANADIAN MATHEMATICAL BULLETIN, 1970, 13 (01): : 139 - &
  • [9] The Structure of Finite Distributive Lattices
    Shmatkov V.D.
    [J]. Journal of Mathematical Sciences, 2016, 213 (2) : 276 - 280
  • [10] ON THE WIDTHS OF FINITE DISTRIBUTIVE LATTICES
    KAHN, J
    SAKS, M
    [J]. DISCRETE MATHEMATICS, 1987, 63 (2-3) : 183 - 195
12345