isEssentialGame {CoopGame} | R Documentation |
Check if game is essential
Description
Checks if a TU game with n players is essential. We call a game essential, if the value of the grand coalition is greater than the sum of the values of the singleton coalitions. A game is essential, if
v(N) > \sum v({i})
.
For an essential game the imputation set is nonempty and consists of more than one point.
Usage
isEssentialGame(v)
Arguments
v |
Numeric vector of length 2^n - 1 representing the values of the coalitions of a TU game with n players |
Value
TRUE
if the game is essential, else FALSE
.
Author(s)
Michael Maerz
Jochen Staudacher jochen.staudacher@hs-kempten.de
References
Chakravarty S.R., Mitra M. and Sarkar P. (2015) A Course on Cooperative Game Theory, Cambridge University Press, p. 23
Gilles R. P. (2015) The Cooperative Game Theory of Networks and Hierarchies, Springer, p. 18
Examples
library(CoopGame)
isEssentialGame(c(1,2,3,4,4,4,7))
# Example of an essential game
library(CoopGame)
v1 <- c(0,0,0,60,60,60,72)
isEssentialGame(v1)
# Example of a game that is not essential
library(CoopGame)
v2 <- c(30,30,15,60,60,60,72)
isEssentialGame(v2)
# Example of a game that is not essential
library(CoopGame)
v3 <- c(20,20,32,60,60,60,72)
isEssentialGame(v3)
[Package CoopGame version 0.2.2 Index]