isWeaklyConstantSumGame {CoopGame} R Documentation

## Check if game is weakly constant-sum

### Description

Checks if a TU game with n players is weakly constant-sum.
In a weakly constant-sum game for any singleton coalition the sums of the values of that singleton coalition and its complement equal the value of the grand coalition `N`.

### Usage

```isWeaklyConstantSumGame(v)
```

### Arguments

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

### Value

`TRUE` if the game is weakly constant-sum, else `FALSE`.

### Author(s)

Jochen Staudacher jochen.staudacher@hs-kempten.de

### References

Staudacher J. and Anwander J. (2019) "Conditions for the uniqueness of the Gately point for cooperative games", arXiv preprint, arXiv:1901.01485, 10 pages.

### Examples

```library(CoopGame)
v1=c(0,0,0,2,2,2,2)
isWeaklyConstantSumGame(v1)

#Example of a game that is not weakly constant-sum
library(CoopGame)
v2=c(0,0,0,40,30,130,100)
isWeaklyConstantSumGame(v2)

#Another example of a weakly constant-sum game
library(CoopGame)
v3=c(1,1,1,2, 7,7,7,7,7,7, 2,3,3,3, 4)
isWeaklyConstantSumGame(v3)

```

[Package CoopGame version 0.2.2 Index]