isConstantSumGame {CoopGame} R Documentation

## Check if game is constant-sum

### Description

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

### Usage

```isConstantSumGame(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 constant-sum, else `FALSE`.

### Author(s)

Jochen Staudacher jochen.staudacher@hs-kempten.de

### References

Peleg B. and Sudhoelter P. (2007) Theory of cooperative games, 2nd Edition, Springer, p. 11

### Examples

```library(CoopGame)
v=c(0,0,0,2,2,2,2)
isConstantSumGame(v)

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

#Another example of a constant-sum game
library(CoopGame)
v=c(1,1,1,2, 2,2,2,2,2,2, 2,3,3,3, 4)
isConstantSumGame(v)

```

[Package CoopGame version 0.2.2 Index]