isWeaklyConstantSumGame {CoopGame}

Check if game is weakly constant-sum

Description

Checks if a TU game with n players is weakly constant-sum.
In a weakly constant-sum game for any singleton coalition the sums of the values of that singleton coalition and its complement equal the value of the grand coalition N.

Usage

isWeaklyConstantSumGame(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 weakly constant-sum, else FALSE.

Author(s)

Jochen Staudacher [e-mail]

References

Staudacher J. and Anwander J. (2019) "Conditions for the uniqueness of the Gately point for cooperative games", arXiv preprint, arXiv:1901.01485, 10 pages.

Examples

library(CoopGame)
v1=c(0,0,0,2,2,2,2) 
isWeaklyConstantSumGame(v1)


#Example of a game that is not weakly constant-sum 
library(CoopGame)
v2=c(0,0,0,40,30,130,100) 
isWeaklyConstantSumGame(v2)

#Another example of a weakly constant-sum game
library(CoopGame)
v3=c(1,1,1,2, 7,7,7,7,7,7, 2,3,3,3, 4)
isWeaklyConstantSumGame(v3)