solidarityvalue {TUGLab} | R Documentation |
Solidarity value
Description
Given a game, this function computes its solidarity value.
Usage
solidarityvalue(v, binary = FALSE, amc = FALSE)
Arguments
v |
A characteristic function, as a vector. |
binary |
A logical value. By default, |
amc |
A logical value. By default, |
Details
Given v\in G^N
, the average marginal contribution to coalition S\in 2^N
is defined as
AMC(S)=\frac{1}{|S|}\sum_{k\in S}(v(S)-v(S\backslash \{k\})).
The solidarity value of each player i \in N
can be defined as
\phi_i(v)=\sum_{S : i\in S}\frac{(n-|S|)!(|S|-1)!}{|N|!}AMC(S).
Value
The solidarity value of the game, as a vector. If amc=TRUE
, a vector (in binary order if binary=TRUE
and in lexicographic order otherwise) containing the average marginal contribution to each coalition is also returned.
References
Nowak, A. S. & Radzik, T. (1994). A solidarity value for n-person transferable utility games. International Journal of Game Theory, 23, 43-48.
See Also
Examples
solidarityvalue(c(0,0,0,1,1,1,2), binary=TRUE)
solidarityvalue(bin2lex(c(0,0,1,2,5,5,7)))
solidarityvalue(bin2lex(c(0,0,2,7,9,10,12,9,11,12,14,19,21,22,24)), amc=TRUE)