A new basis and the Shapley value

被引：6

作者：

Yokote, Koji ^{[1
]}

Funaki, Yukihiko ^{[2
]}

Kamijo, Yoshio ^{[3
]}

机构：

[1] Waseda Univ, Grad Sch Econ, Shinjuku Ku, 1-6-1 Nishi Waseda, Tokyo 1698050, Japan

[2] Waseda Univ, Fac Polit Sci & Econ, Shinjuku Ku, 1-6-1 Nishi Waseda, Tokyo 1698050, Japan

[3] Kochi Univ Technol, Sch Econ & Management, 2-22 Eikokuji, Kochi, Kochi 7808515, Japan

来源：

MATHEMATICAL SOCIAL SCIENCES | 2016年 / 80卷

关键词：

GAMES;

D O I：

10.1016/j.mathsocsci.2015.12.003

中图分类号：

F [经济];

学科分类号：

02 ;

摘要：

The purpose of this paper is to introduce a new basis of the set of all TU games. Shapley (1953) introduced the unanimity game in which cooperation of all players in a given coalition yields payoff. We introduce the commander game in which only one player in a given coalition yields payoff. The set of the commander games forms a basis and has two properties. First, when we express a game by a linear combination of the basis, the coefficients related to singletons coincide with the Shapley value. Second, the basis induces the null space of the Shapley value. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：21 / 24

页数：4

共 50 条

[11] Young's axiomatization of the Shapley value: a new proof
Pinter, Miklos
ANNALS OF OPERATIONS RESEARCH, 2015, 235 (01) : 665 - 673
[12] Young’s axiomatization of the Shapley value: a new proof
Miklós Pintér
Annals of Operations Research, 2015, 235 : 665 - 673
[13] The Shapley value, the Proper Shapley value, and sharing rules for cooperative ventures
van den Brink, Rene
Levinsky, Rene
Zeleny, Miroslav
OPERATIONS RESEARCH LETTERS, 2020, 48 (01) : 55 - 60
[14] Marginalism and the Shapley value
Ghintran, Amandine
REVUE D ECONOMIE POLITIQUE, 2011, 121 (02): : 155 - 177
[15] On the Aumann–Shapley value
Achille Basile
Camillo Costantini
Paolo Vitolo
Positivity, 2008, 12 : 613 - 629
[16] On the interval Shapley value
Gok, S. Z. Alparslan
OPTIMIZATION, 2014, 63 (05) : 747 - 755
[17] UNCERTAINTY OF THE SHAPLEY VALUE
Kargin, Vladislav
INTERNATIONAL GAME THEORY REVIEW, 2005, 7 (04) : 517 - 529
[18] NOTE ON THE SHAPLEY VALUE
OWEN, G
MANAGEMENT SCIENCE, 1968, 14 (11) : 731 - 732
[19] The Shapley Value for Multigraphs
Forlicz, Stefan
Mercik, Jacek
Stach, Izabella
Ramsey, David
COMPUTATIONAL COLLECTIVE INTELLIGENCE, ICCCI 2018, PT II, 2018, 11056 : 213 - 221
[20] Transversality of the Shapley value
Stefano Moretti
Fioravante Patrone
TOP, 2008, 16

← 1 2 3 4 5 →