2 The Mathematics of Power 2.1 An Introduction to Weighted Voting 2.2 The Banzhaf Power Index 2.3 Applications of the Banzhaf Power Index 2.4 The Shapley-Shubik Power Index 2.5 Applications of the Shapley-Shubik Power Index Excursions in Modern Mathematics, 7e: 2.4 - 3 Copyright © 2010 Pears...
Shapley-Shubik indexThis work focuses on multi-type games in which there are a number of non-ordered types in the input, while the output consists of a single real value. When considering the dichotomous case, we extend the Shapley–Shubik power index and provide a full characterization of ...
3.Shapley Value &Shapley-Shubik Power Index Shapley值法大概是Shapley最著名的工作。但是很遗憾并没有因此获诺奖(我个人认为这个概念的重要性不仅无法跟Nash equilibrium相提并论,大概也比不上core)。Shapley和Shubik将Shapley值应用于政治科学中票数的权力度量问题,创立了著名的Shapley-Shubik指数,成为该领域最重要的...
The Shapley–Shubik index is a specialization of the Shapley value and is widely applied to evaluate the power distribution in committees drawing binary decisions. It was generalized to decisions with more than two levels of approval both in the input and the output. The corresponding games are ...
The pivotal role of players is analysed by means of several examples and an axiomatization in the spirit of Shapley and Dubey is given for the proposed power index. 展开 关键词: Theoretical or Mathematical/ game theory/ Shapley-Shubik power index voting system game theory qualitative alternatives...
The Shapley-Shubik power index for games with several levels of approval in the input and output. Decis Support Syst, 2005, 39: 185–195 1314 中国科学 : 信息科学 第 52 卷第 7 期 28 Grabisch M, Lange F. Games on lattices, multichoice games and the shapley value: a new approach. ...
1) Shapley-Shubik Power Index 夏普里舒比克权力指数2) Sharpe index 夏普指数 1. The commonly used appraisal indexes of risk and benefit of open-ended funds including Sharpe index,Treynor index and Jensen index. 开放式基金常用的风险收益评价指标有夏普指数、特雷诺指数和詹森指数,本文比较分析了上述...
(Driessen, 1988), i.e., particularly the kernel, nucleolus, bargaining set, core, the von Neumann–Morgenstern solution (also known as the stable set), the Shapley value (Aumann and Dreze, 1974), the strong epsilon-core (Shapley and Shubik, 1966), and the core of a simple game with ...
In what became known as the Shapley-Shubik index, the Shapley value became the default guide to analyzing all kinds of electoral situations. “He came up with a concept and proved mathematically that the voters in the medium-sized states have more power in the election of a president,” Pete...
In this paper we propose a simple axiom which, along with the axioms of additivity (transfer) and dummy player, characterizes the Shapley value (the Shapley–Shubik power index) on the domain of TU (simple) games. The new axiom, cross invariance, demands payoff invariance on symmetric players...