harsanyidividend {TUGLab} | R Documentation |
Harsanyi dividend
Description
This function computes the Harsanyi dividend of the given coalition in the given game.
Usage
harsanyidividend(v, S, binary = FALSE)
Arguments
v |
A characteristic function, as a vector. |
S |
The position of a coalition, as an integer. |
binary |
A logical value. By default, |
Details
The Harsanyi dividends of v\in G^N
are the coordinates of the game in the base of unanimity games.
They are defined, for all S\in 2^N
, by
c_S=\sum_{S'\subset S}(-1)^{|S|-|S'|}v(S')
.
Value
The Harsanyi dividend of the coalition that occupies the given position in the given order.
References
Hammer, P.J., Peled, U.N., & Sorensen, S. (1977). Pseudo-boolean function and game theory I. Core elements and Shapley value. Cahiers du Centre d'Etudes de Recherche Opérationnelle, 19, 156-176.
See Also
Examples
n <- 3
v <- c(1, 5, 10, 7, 11, 15, 16) # introduced in lexicographic order
coalitionsvector<-character()
dividendsvector<-numeric()
for (i in 1:(2^n-1)){
coalitionsvector <- c(coalitionsvector,
paste(getcoalition(i)[getcoalition(i) != 0],collapse = " "))
dividendsvector <- c(dividendsvector,
harsanyidividend(v, codelex2bin(n,i), binary = FALSE))
}
data.frame(Coalition = coalitionsvector, Dividend = dividendsvector)
data.frame(Coalition = bin2lex(coalitionsvector), Dividend = bin2lex(dividendsvector))