TUGLab (version 0.0.1)

myersonvalue: Myerson value

Description

Given a game and a communications network, this function computes the Myerson value.

Usage

myersonvalue(v, binary = FALSE, communications, game = FALSE)

Value

The corresponding Myerson value, as a vector.

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.

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 communications is not specified, it is assumed that all players can communicate with each other.

game

A logical value. By default, game=FALSE. If set to TRUE, the game with restricted communication is also returned.

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 \(v^{A}\).

References

Myerson, R. B. (1977). Graphs and cooperation in games. Mathematics of Operations Research, 2(3), 225-229.

See Also

shapleyvalue

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)