isWeaklySuperadditiveGame {CoopGame}

Check if game is weakly superadditive

Description

Checks if a TU game with n players is weakly superadditive.
Let S be a coalition and i a player not contained in S. Then the TU game is weakly superadditive if for any S and any i the value of the union of S and i is greater or equal the sum of the values of S and i.
Note that weak superadditivity is equivalent to zero-monotonicity.

Usage

isWeaklySuperadditiveGame(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 superadditive, else FALSE.

Author(s)

Johannes Anwander [e-mail]

Jochen Staudacher [e-mail]

References

Peleg B. and Sudhoelter P. (2007) Theory of cooperative games, 2nd Edition, Springer, p. 10

Examples

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


#Example of a weakly superadditive game
library(CoopGame)
v1=c(1:15)
isWeaklySuperadditiveGame(v1)

#Example of a game which is not weakly superadditive
library(CoopGame)
v2=c(1:5,7,7)
isWeaklySuperadditiveGame(v2)