# Owen_value: Owen_value (Owen value) In GameTheoryAllocation: Tools for Calculating Allocations in Game Theory

## Description

This function gives the Owen value described in Owen (1977).

## Usage

 `1` ```Owen_value(characteristic_function, union, game = c("profit", "cost")) ```

## Arguments

 `characteristic_function` A vector with the characteristic function v(S) (or c(S), if we work with a cost game), according to the order of coalitions shown in `coalitions` function. `union` A list with a partition of the players set. Each element of this list is a union a priori, following the proposal of Owen. `game` Characters to indicate if the game is a cost or profit game. The possibles values are `"cost"` or `"profit"`.

## Value

A vector with the allocation that Owen value (Owen, 1977) proposes.

## Author(s)

A. Saavedra-Nieves

## References

Owen, G. (1977). Values of games with a priori unions. Mathematical Economics and Game Theory: Essays in Honor of Oskar Morgenstern (Eds.: O. Moeschlin R. Hein). Springer, New York.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```characteristic_function<-c(1,1,2,1,2,2,2) Owen_value(characteristic_function,union=list(c(1,2),c(3)),game="cost") #[1] "Owen Value" # 1 2 3 # 0.25 0.25 1.5 Shapley_value(characteristic_function,game="cost") #[1] "Shapley Value" # 1 2 3 # 0.3333333 0.3333333 1.333333 ```

### Example output

```Loading required package: e1071