isAdditiveGame: Check if game is additive
In CoopGame: Important Concepts of Cooperative Game Theory

Description Usage Arguments Value Author(s) References Examples

Checks if a TU game with n players is additive.
In an additive game for any two disjoint coalitions S and T the value of the union of S and T equals the sum of the values of S and T. In other words, additive games are constant-sum and the imputation set of an additive game consists of exactly one point.

1	isAdditiveGame(v)

`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 additive, else FALSE

Alexandra Tiukkel

Jochen Staudacher jochen.staudacher@hs-kempten.de

Peleg B. and Sudhoelter P. (2007) Theory of cooperative games, 2nd Edition, Springer, p. 11

Peters H. (2015) Game Theory: A Multi-Leveled Approach, 2nd Edition, Springer, p. 292

Osborne M.J. and Rubinstein A. (1994) A Course in Game Theory, MIT Press, p. 261

library(CoopGame)
isAdditiveGame(c(1,1,1,2,2,2,3))


#The following game is not additive
library(CoopGame)
v=c(0,0,0,40,50,20,100)
isAdditiveGame(v) 

#The following game is additive
library(CoopGame)
v=c(1,1,1,1, 2,2,2,2,2,2, 3,3,3,3, 4)
isAdditiveGame(v)