colemanCollectivityPowerIndex: Compute Coleman Power index of a Collectivity to Act

In CoopGame: Important Concepts of Cooperative Game Theory

Description

Calculates the Coleman Power index of a Collectivity to Act for a specified simple TU game. Note that in general the Coleman Power index of a Collectivity to Act is not an efficient vector, i.e. the sum of its entries is not always 1. Note also that the the Coleman Power index of a Collectivity to Act is identical for each player, i.e. the result for each player is the number of winning coalitions divided by 2^n. Hence no drawing routine for the Coleman Power index of a Collectivity to Act is provided.

Usage

colemanCollectivityPowerIndex(v)

Arguments

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

Value

Coleman Power index of a Collectivity to Act for specified simple game

Author(s)

Jochen Staudacher [e-mail]

References

Coleman J.S. (1971) "Control of collectivities and the power of a collectivity to act". In: Liberman B. (Ed.), Social Choice, Gordon and Breach, pp. 269–300

De Keijzer B. (2008) "A survey on the computation of power indices", Technical Report, Delft University of Technology, p. 18

Bertini C. and Stach I. (2011) "Coleman index", Encyclopedia of Power, SAGE Publications, p. 117–119

Examples

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

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