webersetVertices {CoopGame} R Documentation

## Compute vertices of Weber Set

### Description

Calculates the Weber Set for given game vector with n players.

### Usage

```webersetVertices(v)
```

### Arguments

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

### Value

rows of the matrix are the vertices of the Weber Set

### Author(s)

Anna Merkle

Franz Mueller

Jochen Staudacher jochen.staudacher@hs-kempten.de

### References

Weber R.J. (1988) "Probabilistic values for games". In: Roth A.E. (Ed.), The Shapley Value. Essays in in honor of Lloyd S. Shapley, Cambridge University Press, pp. 101–119

Peters H. (2015) Game Theory: A Multi-Leveled Approach, 2nd Edition, Springer, pp. 327–329

### Examples

```library(CoopGame)
webersetVertices(c(0,0,0,1,1,1,2))

#Example of a 3-player TU game (with a Weber Set with 6 vertices)
library(CoopGame)
v = c(0,1,2,3,4,5,6)
webersetVertices(v)

#Example of a 4-player TU game (with a Weber Set with 14 vertices)
library(CoopGame)
v = c(5,2,4,7,15,15,15,15,15,15,20,20,20,20,35)
webersetVertices(v)

```

[Package CoopGame version 0.2.2 Index]