getMinimumWinningCoalitions {CoopGame} R Documentation

## Compute minimal winning coalitions in a simple game

### Description

The function getMinimumWinningCoalitions identifies all minimal winning coalitions of a specified simple game. These coalitions are characterized by the circumstance that if any player breaks away from them, then the coalition generates no value (then also called a losing coalition) - all players in the coalition can therefore be described as critical players.

### Usage

```getMinimumWinningCoalitions(v)
```

### Arguments

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

### Value

A data frame containing all minimum winning coalitions for a simple game.

### Author(s)

Johannes Anwander anwander.johannes@gmail.com

Jochen Staudacher jochen.staudacher@hs-kempten.de

### References

Deegan J. and Packel E.W. (1978) "A new index of power for simple n-person games", Int. Journal of Game Theory 7(2), pp. 151–161

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

Bertini C. (2011) "Minimal winning coalition", Encyclopedia of Power, SAGE Publications, pp. 422–423

### Examples

```library(CoopGame)
getMinimumWinningCoalitions(v=c(0,0,0,0,0,0,1))

library(CoopGame)
v=weightedVotingGameVector(n=3,w=c(1,2,3),q=5)
getMinimumWinningCoalitions(v)
# Output:
#   V1 V2 V3 cVal
# 6  0  1  1    1
# => the coalition containing player 2 and 3 is a minimal winning coalition

```

[Package CoopGame version 0.2.2 Index]