Given a game and a permutation, this function returns the corresponding marginal contributions vector.
Usage
marginalvector(v, binary = FALSE, permutation)
Value
The vector of marginal contributions.
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 \(Pre^{\pi}(i)=\{j:\pi(j)<\pi(i)\}\).
n <- 3
v <- c(1, 5, 10, 30, 60, 90, 200)
for (i in1:factorial(n)) {
cat("[", i, "]", paste(getpermutation(3,i))," ",
paste(marginalvector(v,binary=FALSE,i)), "\n")
}