apexGame {CoopGame} R Documentation

## Construct an apex game

### Description

Create a list containing all information about a specified apex game:
A coalition can only win (and hence obtain the value `1`) if it
a) contains both the apex player and one additional player
or
b) contains all players except for the apex player.
Any non-winning coalitions obtain the value `0`.
Note that apex games are always simple games.

### Usage

```apexGame(n, apexPlayer)
```

### Arguments

 `n` represents the number of players `apexPlayer` specifies the number of the apex player

### Value

A list with three elements representing the apex game (n, apexPlayer, Game vector v)

### Author(s)

Jochen Staudacher jochen.staudacher@hs-kempten.de

Johannes Anwander anwander.johannes@gmail.com

### References

Peters H. (2015) Game Theory: A Multi-Leveled Approach, 2nd Edition, Springer, pp. 164–165

### Examples

```library(CoopGame)
apexGameVector(n=3,apexPlayer=2)

library(CoopGame)
#Example with four players, apex player is number 3
(vv<-apexGame(n=4,apexPlayer=3))
#\$n
#[1] 4

#\$apexPlayer
#[1] 4

#\$v
# [1] 0 0 0 0 0 1 0 1 0 1 1 1 1 1 1

```

[Package CoopGame version 0.2.2 Index]