publicHelpIndex: Compute Public Help index Theta

In CoopGame: Important Concepts of Cooperative Game Theory

Description

Calculates the Public Help index Theta for a specified simple TU game. Note that the Public Help index Theta goes back to the paper by Bertini, Gambarelli and Stach (2008) and is frequently simply referred to referred to Public Help index in the literature.

Usage

publicHelpIndex(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 Theta for specified simple game

Author(s)

Johannes Anwander [e-mail]

Jochen Staudacher [e-mail]

References

Bertini C., Gambarelli G. and Stach I. (2008) "A public help index", In: Braham, M. and Steffen, F. (Eds): Power, freedom, and voting: Essays in Honour of Manfred J. Holler, pp. 83–98

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)
publicHelpIndex(v=c(0,0,0,0,1,0,1))


#Example from paper by Stach (2016), p. 105:
library(CoopGame)
v=c(0,0,0,1,1,0,1)
publicHelpIndex(v) 
#result: 0.4285714 0.2857143 0.2857143

#Second example from 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)
publicHelpIndex(v)
#result: 0.3529412 0.2352941 0.2352941 0.1764706

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