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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 vGN. Assuming that communication between players is necessary for their cooperation, the game with restricted communication, vA, is defined by vA(S)=v(S) if the players of S can communicate and vA(S)=0 otherwise, for each S2N.

The Myerson value is the Shapley value of the game vA.

References

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

See Also

shapleyvalue

Examples

Run this code
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)

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