publicHelpIndex {CoopGame} | R Documentation |
Compute Public Help index Theta
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 anwander.johannes@gmail.com
Jochen Staudacher jochen.staudacher@hs-kempten.de
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