coreVertices {CoopGame} R Documentation

## Compute core vertices

### Description

Calculates the core vertices for given game vector

### Usage

```coreVertices(v)
```

### Arguments

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

### Value

rows of the matrix are the vertices of the core

### Author(s)

Franz Mueller

Jochen Staudacher jochen.staudacher@hs-kempten.de

### References

Gillies D.B. (1953) Some Theorems on n-person Games, Ph.D. Thesis, Princeton University Press.

Aumann R.J. (1961) "The core of a cooperative game without side payments", Transactions of the American Mathematical Society 98(3), pp. 539–552

Peleg B. and Sudhoelter P. (2007) Theory of cooperative games, 2nd Edition, Springer, pp. 27–49

Maschler M., Solan E. and Zamir S. (2013) Game Theory, Cambridge University Press, pp. 686–747

Osborne M.J. and Rubinstein A. (1994) A Course in Game Theory, MIT Press, pp. 257–275

### Examples

```library(CoopGame)
coreVertices(c(0,0,0,1,1,1,3))

#In the following case the core consists of a single point
v1 = c(0,1,2,3,4,5,6)
coreVertices(v1)
#     [,1] [,2] [,3]
#[1,]    1    2    3

#Users may also want to try the following commands:
coreVertices(c(0,0,0,60,80,100,135))
coreVertices(c(5,2,4,7,15,15,15,15,15,15,20,20,20,20,35))
coreVertices(c(0,0,0,0,0,5,5,5,5,5,5,5,5,5,5,15,15,15,15,15,15,15,15,15,15,30,30,30,30,30,60))

```

[Package CoopGame version 0.2.2 Index]