Description Usage Arguments Value Author(s) References Examples
View source: R/GamePropertyEssentiality.R
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) > ∑ v({i})
.
For an essential game the imputation set is nonempty and consists of more than one point.
1 |
v |
Numeric vector of length 2^n - 1 representing the values of the coalitions of a TU game with n players |
TRUE
if the game is essential, else FALSE
.
Michael Maerz
Jochen Staudacher jochen.staudacher@hs-kempten.de
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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | 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)
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