isSimpleGame {CoopGame}

Check if game is simple

Description

isSimpleGame checks if a TU game is a simple game. A TU game is a simple game in the sense of the book by Peleg and Sudhoelter (2007), p. 16, if and only if the game is monotonic and the values of all coalitions are either 0 or 1.

Usage

isSimpleGame(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)

Jochen Staudacher [e-mail]

References

Peleg B. and Sudhoelter P. (2007) Theory of cooperative games, 2nd Edition, Springer, p. 16

Examples

library(CoopGame)
isSimpleGame(c(0,0,0,1,0,1,1))


#Example of a simple game
library(CoopGame) 
v1<-c(0,0,0,0,1,1,1)
isSimpleGame(v1)

#Example of a game which not simple 
library(CoopGame)
v2<-c(0,0,0,0,1,1,2)
isSimpleGame(v2)

#Another example of a game which not simple 
#according to our definition
library(CoopGame) 
v3<-c(1,0,0,0,1,1,1)
isSimpleGame(v3)