isSuperadditiveGame {CoopGame} R Documentation

## Check if game is superadditive

### Description

Checks if a TU game with n players is superadditive.
In a superadditive game for any two disjoint coalitions `S` and `T` the value of the union of `S` and `T` is always greater or equal the sum of the values of `S` and `T`. In other words, the members of any two disjoint coalitions `S` and `T` will never be discouraged from collaborating.

### Usage

```isSuperadditiveGame(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 superadditive, else `FALSE`.

### Author(s)

Alexandra Tiukkel

Jochen Staudacher jochen.staudacher@hs-kempten.de

### References

Peleg B. and Sudhoelter P. (2007) Theory of cooperative games, 2nd Edition, Springer, p. 10

Peters H. (2015) Game Theory: A Multi-Leveled Approach, 2nd Edition, Springer, p. 295

Maschler M., Solan E. and Zamir S. (2013) Game Theory, Cambridge University Press, p. 671

Narahari Y. (2015) Game Theory and Mechanism Design, World Scientific Publishing, p. 408

### Examples

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

#Example of a superadditive game
library(CoopGame)
v1=c(0,0,0,40,50,20,100)
isSuperadditiveGame(v1)

#Example of a game that is not superadditive
library(CoopGame)
v2=c(0,0,0,40,30,130,100)
isSuperadditiveGame(v2)

#Another example of a superadditive game
library(CoopGame)
v3=c(1,1,1,1, 2,2,2,2,2,2, 3,3,3,3, 4)
isSuperadditiveGame(v3)

```

[Package CoopGame version 0.2.2 Index]