superadditivecheck {TUGLab} | R Documentation |
Superadditive check
Description
This function checks if the given game is superadditive.
Usage
superadditivecheck(v, binary = FALSE, instance = FALSE)
Arguments
v |
A characteristic function, as a vector. |
binary |
A logical value. By default, |
instance |
A logical value. By default, |
Details
A game v\in G^N
is superadditive if v(S \cup T) \ge v(S)+v(T)
for all S,T \in 2^N
with S \cap T = \emptyset
.
A game v\in G^N
is subadditive if -v
is superadditive.
Value
TRUE
if the game is superadditive, FALSE
otherwise. If instance=TRUE
and the game is not superadditive, the function also returns the positions (binary order positions if binary=TRUE
; lexicographic order positions otherwise) of a pair of coalitions violating superadditivity.
See Also
additivecheck, convexcheck, monotoniccheck, strategicallyequivalentcheck
Examples
v <- c(2, 2, 4, 2, 4, 5, 6)
superadditivecheck(v, binary = TRUE, instance = TRUE)
# How to check if a game is subadditive:
v.sub <- c(40, 30, 50, 60, 70, 65, 90) # subadditive game
superadditivecheck(-v.sub)