isBalancedGame {CoopGame} R Documentation

## Check if game is balanced

### Description

Checks if a game is balanced. A game is balanced if the core is a nonempty set.

### Usage

```isBalancedGame(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 balanced, else `FALSE`

### Author(s)

Jochen Staudacher jochen.staudacher@hs-kempten.de

### References

Bondareva O.N. (1963) "Some applications of linear programming methods to the theory of cooperative games". Problemy kibernetiki 10, pp. 119–139

Shapley L.S. (1967) "On Balanced Sets and Cores". Naval Research Logistics Quarterly 14, pp. 453–460

Peleg B. and Sudhoelter P. (2007) Theory of cooperative games, 2nd Edition, Springer, pp. 27–32

Maschler M., Solan E. and Zamir S. (2013) Game Theory, Cambridge University Press, pp. 691–702

Slikker M. and van den Nouweland A. (2001) Social and Economic Networks in Cooperative Game Theory, Springer, pp. 6–7

Osborne M.J. and Rubinstein A. (1994) A Course in Game Theory, MIT Press, pp. 262–263

### Examples

```library(CoopGame)
v=c(0,0,0,40,50,20,100)
isBalancedGame(v)

#Example of an unbalanced game with 3 players
library(CoopGame)
v=c(1,1,1,2,3,4,3)
isBalancedGame(v)

#Example of an unbalanced game with 4 players
library(CoopGame)
v=c(0,0,0,0,1,0,0,0,0,3,3,3,3,3,4)
isBalancedGame(v)

#Example of a balanced game with 4 players
library(CoopGame)
v= c(0,0,0,0,1,0,0,0,0,2,2,2,2,2,4)
isBalancedGame(v)

```

[Package CoopGame version 0.2.2 Index]