publicHelpChiIndex: Compute Public Help index Chi

In CoopGame: Important Concepts of Cooperative Game Theory

Description

Calculates the Public Help index Chi for a specified simple TU game. Note that the greek letter Xi (instead of Chi) was used in the original paper by Bertini and Stach (2015).

Usage

publicHelpChiIndex(v)

Arguments

v	Numeric vector of length 2^n - 1 representing the values of the coalitions of a TU game with n players

Value

Public Help index Chi for specified simple game

Author(s)

Jochen Staudacher [e-mail]

References

Bertini C. and Stach I. (2015) "On Public Values and Power Indices", Decision Making in Manufacturing and Services 9(1), pp. 9–25

Stach I. (2016) "Power Measures and Public Goods", In: Nguyen, N.T. and Kowalczyk, R. (Eds.): Transactions on Computational Collective Intelligence XXIII, Springer, pp. 99–110

Examples

library(CoopGame)
publicHelpChiIndex(v=c(0,0,0,0,1,0,1))


#Example from original paper by Stach (2016), p. 105:
library(CoopGame)
v=c(0,0,0,1,1,0,1)
publicHelpChiIndex(v) 
#result: 0.4583333 0.2708333 0.2708333

#Second example from original paper by Stach (2016), p. 105:
library(CoopGame)
v=c(0,0,0,0,1,1,0,0,0,0,1,1,1,0,1)
publicHelpChiIndex(v)
#result: 0.3981481 0.2376543 0.2376543 0.1265432

CoopGame documentation built on Aug. 24, 2021, 1:07 a.m.