marginalgame {TUGLab} | R Documentation |
Marginal game
Description
Given a game and a coalition, this function returns the characteristic function of the corresponding marginal game.
Usage
marginalgame(v, S, binary = FALSE)
Arguments
v |
Characteristic function, as a vector. |
S |
The position of a coalition, as an integer. |
binary |
A logical value. By default, |
Details
Given a game v\in G^N
and a coalition S\in 2^N
, the S-marginal game, v^S\in G^N
,
is defined by
v^S(R)=v(R\cup (N\backslash S))-v(N\backslash S)+v(R\cap (N\backslash S))\text{ for all }R\in 2^N.
Value
The characteristic function of the S
-marginal game, as a vector in binary order if binary=TRUE
and in lexicographic order otherwise.
References
Sánchez Rodríguez, E., Mirás Calvo, M.A., Quinteiro Sandomingo, C., & Núñez Lugilde, I. (2024). Coalition-weighted Shapley values. International Journal of Game Theory 53, 547-577.
Examples
v <- c(0, 0, 0, 2, 3, 10, 20)
marginalgame(v, 5, binary = TRUE) # coalition {1,3}
n <- 3
for (i in 1:(2^n - 1)) {
cat("[", i, "]", paste(marginalgame(lex2bin(v),codebin2lex(n,i),binary=TRUE)),"\n")
}
for (i in 1:(2^n - 1)) {
cat("[", i, "]", paste(marginalgame(v,i)),"\n")
}