marginalvector {TUGLab}R Documentation

Marginal contributions vector

Description

Given a game and a permutation, this function returns the corresponding marginal contributions vector.

Usage

marginalvector(v, binary = FALSE, permutation)

Arguments

v

A characteristic function, as a vector.

binary

A logical value. By default, binary=FALSE. Should be set to TRUE if v is introduced in binary order instead of lexicographic order.

permutation

Position of the permutation in the Lehmer code order, as an integer.

Details

Given a game v\in G^N and an order \pi of the players in N, the marginal contributions associated with order \pi is defined, for all i \in N, as m_i^{\pi}=v(Pre^{\pi}(i)\cap i)-v(Pre^{\pi}(i)), being Pre^{\pi}(i)=\{j:\pi(j)<\pi(i)\}.

Value

The vector of marginal contributions.

See Also

getpermutation, getpermutationnumber

Examples

n <- 3
v <- c(1, 5, 10, 30, 60, 90, 200)
for (i in 1:factorial(n)) {
  cat("[", i, "]", paste(getpermutation(3,i)),"  ",
  paste(marginalvector(v,binary=FALSE,i)), "\n")
}

[Package TUGLab version 0.0.1 Index]