CoopGame (version 0.2.2)

isAdditiveGame: 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

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

# NOT RUN {
library(CoopGame)
isAdditiveGame(c(1,1,1,2,2,2,3))

# }
# NOT RUN {
#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)
# }
# NOT RUN {
# }