The Shapley value

Description

Computes the Shapley value (n indices) of a set function. The set function can be given either under the form of an object of class set.func, card.set.func or Mobius.set.func.

Methods

object = "Mobius.set.func"

The Shapley value is computed from the M<c3><b6>bius transform of a set function.

object = "card.set.func"

The Shapley value is computed from a cardinal set function.

object = "set.func"

The Shapley value is computed from a general set function.

References

L.S. Shapley (1953), A value for n-person games, Contributions to the theory of games, vol. 2, Annals of Mathematics Studies, no. 28, pages 307-317, Princeton University Press, Princeton, N. J. .

See Also

Mobius.set.func-class,
card.set.func-class,
set.func-class,
Mobius-methods.

Examples

## a set function
mu <- set.func(c(0:13/13,1,1))

## the Shapley value
Shapley.value(mu)

## the efficiency property should be satisfied
sum(Shapley.value(mu))

## a similar example using a Mobius.set.func object
a <- Mobius(mu)
Shapley.value(a)

## a similar example using a card.set.func object
mu <- upper.capacity(6)
Shapley.value(mu)
## the efficiency property should be satisfied
Shapley.value(mu)*6

Results