shapleyValue: Shapley value of a cooperative game
In cooptrees: Cooperative aspects of optimal trees in weighted graphs

Description Usage Arguments Details Value References Examples

Given a cooperative game, the shapleyValue function computes its Shapley value.

1	shapleyValue(n, S = NULL, v)

`n`	number of players in the cooperative game.
`S`	vector with all the possible coalitions. If none has been specified the function generates it automatically.
`v`	vector with the characteristic function of the cooperative game.

The Shapley value is a solution concept in cooperative game theory proposed by Lloyd Shapley in 1953. It is obtained as the average of the marginal contributions of the players associated with all the posible orders of the players.

The shapleyValue functions returns a matrix with all the marginal contributions of the players (contributions) and a vector with the Shapley value (value).

Lloyd S. Shapley. "A Value for n-person Games". In Contributions to the Theory of Games, volume II, by H.W. Kuhn and A.W. Tucker, editors. Annals of Mathematical Studies v. 28, pp. 307-317. Princeton University Press, 1953.

# Cooperative game
n <- 3  # players
v <- c(4, 4, 4, 8, 8, 8, 14)  # characteristic function
# Shapley value
shapleyValue(n, v = v)

Loading required package: igraph

Attaching package: 'igraph'

The following objects are masked from 'package:stats':

    decompose, spectrum

The following object is masked from 'package:base':

    union

Loading required package: optrees
$contributions
     [,1] [,2] [,3]
[1,]    4    4    6
[2,]    4    6    4
[3,]    4    4    6
[4,]    6    4    4
[5,]    4    6    4
[6,]    6    4    4

$value
[1] 4.666667 4.666667 4.666667