# shapleyValue: Shapley value of a cooperative game

## Description

Given a cooperative game, the `shapleyValue`

function
computes its Shapley value.
## Usage

shapleyValue(n, S = NULL, v)

## Arguments

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.

## Value

The `shapleyValue`

functions returns a matrix with all
the marginal contributions of the players
(`contributions`

) and a vector with the Shapley value
(`value`

).

## Details

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.
## References

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.
## Examples

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