GameTheoryAllocation (version 1.0)

Owen_value: Owen_value (Owen value)

Description

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

Usage

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.

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

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