shapleyValue
From cooptrees v1.0
by Manuel Fontenla
Shapley value of a cooperative game
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.
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.
Value

The
shapleyValue
functions returns a matrix with all
the marginal contributions of the players
(contributions
) and a vector with the Shapley value
(value
).
References
Lloyd S. Shapley. "A Value for nperson 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. 307317. 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)
Community examples
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