weightedVotingGame {CoopGame} R Documentation

## Construct a weighted voting game

### Description

Create a list containing all information about a specified weighted voting game:
For a weighted voting game we receive a game vector where each element contains `1` if the sum of the weights of coalition `S` is greater or equal than quota `q`, else `0`.
Note that weighted voting games are always simple games.

### Usage

```weightedVotingGame(n, w, q)
```

### Arguments

 `n` represents the number of players `w` numeric vector which contains the weight of each player `q` is the quota

### Value

A list with four elements representing the weighted voting game (n, w, q, Game vector v)

### Author(s)

Jochen Staudacher jochen.staudacher@hs-kempten.de

### References

Peleg B. (2002) "Game-theoretic analysis of voting in committees". in: Handbook of Social Choice and Welfare 1, pp. 195–201

Peleg B. and Sudhoelter P. (2007) Theory of cooperative games, 2nd Edition, Springer, p. 17

Maschler M., Solan E. and Zamir S. (2013) Game Theory, Cambridge University Press, pp. 825–831

### Examples

```library(CoopGame)
weightedVotingGame(n=3,w=c(1,2,3),q=4)

library(CoopGame)
weightedVotingGame(n=4,w=c(1,2,3,4),q=5)

#Output:
#\$n
#[1] 4

#\$w
#[1] 1 2 3 4
#
#\$q
#[1] 5
#
#\$v
#[1] 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1

```

[Package CoopGame version 0.2.2 Index]