isSymmetricGame {CoopGame}

Check if game is symmetric

Description

isSymmetricGame checks if a TU game is symmetric. A TU game is symmetric if and only if the values of all coalitions containing the same number of players are identical.

Usage

isSymmetricGame(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 symmetric, else FALSE.

Author(s)

Jochen Staudacher [e-mail]

References

Peleg B. and Sudhoelter P. (2007) Theory of cooperative games, 2nd Edition, Springer, p. 12

Chakravarty S.R., Mitra M. and Sarkar P. (2015) A Course on Cooperative Game Theory, Cambridge University Press, p. 26

Examples

library(CoopGame)
isSymmetricGame(c(0,0,0,1,1,1,2))


#Example of a symmetric game
library(CoopGame) 
v1<-c(3,3,3,10,10,10,17)
isSymmetricGame(v1)

#Example of a game which is not symmetric 
library(CoopGame) 
v2=c(1:7)
isSymmetricGame(v2)