GameTheoryAllocation (version 1.0)

Shapley_value: Shapley_value (Shapley Value)

Description

This function gives the Shapley value introduced in Shapley (1953).

Usage

Shapley_value(characteristic_function, 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.

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 Shapley value (Shapley, 1953) proposes.

References

Shapley, L.S. (1953). A value por n-person games. In H. Kuhn y A. Tucker (eds), Contributions to the theory of games II, Vol. 28, Annals of Mathematics Studies. Princeton University Press.

Examples

characteristic_function<-c(1,1,2,1,2,2,2)
 
Shapley_value(characteristic_function,game="cost")
#[1] "Shapley Value"
#          1         2        3
#  0.3333333 0.3333333 1.333333