| isAdditiveGame {CoopGame} | R Documentation |
Check if game is additive
Description
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.
Usage
isAdditiveGame(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 additive, else FALSE
Author(s)
Alexandra Tiukkel
Jochen Staudacher jochen.staudacher@hs-kempten.de
References
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
Examples
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)