banzhafValue {CoopGame} R Documentation

## Compute Banzhaf value

### Description

banzhafValue computes the Banzhaf value for a specified TU game The Banzhaf value itself is an alternative to the Shapley value.
Conceptually, the Banzhaf value is very similar to the Shapley value. Its main difference from the Shapley value is that the Banzhaf value is coalition based rather than permutation based. Note that in general the Banzhaf vector is not efficient! In this sense this implementation of the Banzhaf value could also be referred to as the non-normalized Banzhaf value, see formula (20.6) in on p. 368 of the book by Hans Peters (2015).

banzhafValue(v)

### Arguments

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

### Value

The return value is a numeric vector which contains the Banzhaf value for each player.

### Author(s)

Johannes Anwander anwander.johannes@gmail.com

Jochen Staudacher jochen.staudacher@hs-kempten.de

### References

Peters H. (2015) Game Theory: A Multi-Leveled Approach, 2nd Edition, Springer, pp. 367–370

Chakravarty S.R., Mitra M. and Sarkar P. (2015) A Course on Cooperative Game Theory, Cambridge University Press, pp. 118–119

Gambarelli G. (2011) "Banzhaf value", Encyclopedia of Power, SAGE Publications, pp. 53–54

### Examples

library(CoopGame)
v=c(0,0,0,1,2,1,4)
banzhafValue(v)

#Example from paper by Gambarelli (2011)
library(CoopGame)
v=c(0,0,0,1,2,1,3)
banzhafValue(v)
#[1] 1.25 0.75 1.25

[Package CoopGame version 0.2.2 Index]