TUGLab (version 0.0.1)

solidarityvalue: Solidarity value

Description

Given a game, this function computes its solidarity value.

Usage

solidarityvalue(v, binary = FALSE, amc = FALSE)

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.

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.

amc

A logical value. By default, amc=FALSE. If set to TRUE, the average marginal contributions are also returned.

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 $$\phi_i(v)=\sum_{S : i\in S}\frac{(n-|S|)!(|S|-1)!}{|N|!}AMC(S).$$

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

shapleyvalue

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)