shapleyShubikIndex {CoopGame} R Documentation

## Compute Shapley-Shubik index

### Description

Calculates the Shapley-Shubik index for a specified simple game with n players. Note that no separate drawing routine for the Shapley-Shubik index is provide as users can always resort to drawShapleyValue

### Usage

```shapleyShubikIndex(v)
```

### Arguments

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

### Value

Shapley-Shubik index for given simple game

### Author(s)

Alexandra Tiukkel

Jochen Staudacher jochen.staudacher@hs-kempten.de

### References

Shapley L.S. and Shubik M. (1954) "A method for evaluating the distribution of power in a committee system". American political science review 48(3), pp. 787–792

Shapley L.S. (1953) "A value for n-person games". In: Kuhn, H., Tucker, A.W. (Eds.), Contributions to the Theory of Games II, Princeton University Press, pp. 307–317

Peters H. (2015) Game Theory: A Multi-Leveled Approach, 2nd Edition, Springer, pp. 156–159

Maschler M., Solan E. and Zamir S. (2013) Game Theory, Cambridge University Press, pp. 748–781

Stach I. (2011) "Shapley-Shubik index", Encyclopedia of Power, SAGE Publications, pp. 603–606

### Examples

```library(CoopGame)
shapleyShubikIndex(v=c(0,0,0,0,1,0,1))

#Example from Stach (2011):
library(CoopGame)
v=weightedVotingGameVector(n=4,q=50,w=c(10,10,20,30))
shapleyShubikIndex(v)
#[1] 0.08333333 0.08333333 0.25000000 0.58333333

```

[Package CoopGame version 0.2.2 Index]