Description Usage Arguments Value Author(s) References Examples
View source: R/GamePropertyWeakSuperadditivity.R
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.
1 |
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 weakly superadditive, else FALSE
.
Johannes Anwander anwander.johannes@gmail.com
Jochen Staudacher jochen.staudacher@hs-kempten.de
Peleg B. and Sudhoelter P. (2007) Theory of cooperative games, 2nd Edition, Springer, p. 10
1 2 3 4 5 6 7 8 9 10 11 12 13 | 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)
|
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