normalizedBanzhafIndex {CoopGame} R Documentation

## Compute normalized Banzhaf index

### Description

Normalized Banzhaf index for a specified simple game, see formula (7.6) on p. 119 of the book by Chakravarty, Mitra and Sarkar

### Usage

```normalizedBanzhafIndex(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 normalized Banzhaf index 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

Bertini C. and Stach I. (2011) "Banzhaf voting power measure", Encyclopedia of Power, SAGE Publications, pp. 54–55

### Examples

```library(CoopGame)
normalizedBanzhafIndex(dictatorGameVector(n=3, dictator=1))

library(CoopGame)
v<-weightedVotingGameVector(n=4,w=c(8,6,4,2),q=c(12))
normalizedBanzhafIndex(v)
#[1] 0.41666667 0.25000000 0.25000000 0.08333333

library(CoopGame)
v<- apexGameVector(n = 4,apexPlayer=3)
normalizedBanzhafIndex(v)
#[1] 0.1666667 0.1666667 0.5000000 0.1666667

library(CoopGame)
#N=c(1,2,3), w=(50,49,1), q=51
v=weightedVotingGameVector(n=3, w=c(50,49,1),q=51)
normalizedBanzhafIndex(v)
#[1] 0.6 0.2 0.2

library(CoopGame)
v<-weightedVotingGameVector(n=3,w=c(50,30,20),q=c(67))
normalizedBanzhafIndex(v)
#[1] 0.6 0.2 0.2

```

[Package CoopGame version 0.2.2 Index]