myersonvalue {TUGLab} | R Documentation |
Myerson value
Description
Given a game and a communications network, this function computes the Myerson value.
Usage
myersonvalue(v, binary = FALSE, communications, game = FALSE)
Arguments
v |
A characteristic function, as a vector. |
binary |
A logical value. By default, |
communications |
An undirected communications network, as a list of vectors (their order being irrelevant), each containing two different players (their order being irrelevant). If two players are able to communicate with each other, a bidimensional vector containing them should be present in the list; otherwise, the vector should be absent. When |
game |
A logical value. By default, |
Details
Let v\in G^N
. Assuming that communication between players is necessary for their cooperation,
the game with restricted communication, v^{A}
, is defined by
v^{A}(S)=v(S)
if the players of S can communicate and v^{A}(S)=0
otherwise, for each S\in 2^N
.
The Myerson value is the Shapley value of the game v^{A}
.
Value
The corresponding Myerson value, as a vector.
References
Myerson, R. B. (1977). Graphs and cooperation in games. Mathematics of Operations Research, 2(3), 225-229.
See Also
Examples
v <- c(0,0,0,0,30,30,40,40,50,50,60,70,80,90,100)
communications <- list(c(1,2), c(1,3), c(1,4))
myersonvalue(v, binary=FALSE, communications)