zeromonotoniccheck {TUGLab} | R Documentation |
0-monotonic check
Description
This function checks if the given game is 0-monotonic.
Usage
zeromonotoniccheck(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 0-monotonic if v_0(S) \le v_0(T)
for all S, T \in 2^N
such that S\subset T
, being v_0\in G^N
the 0-normalization of v
.
Value
TRUE
if the game is 0-monotonic, FALSE
otherwise. If instance=TRUE
and the game is not 0-monotonic, the function also returns the positions (binary order positions if binary=TRUE
; lexicographic order positions otherwise) of a pair of coalitions violating 0-monotonicity.
See Also
monotoniccheck, zeronormalizedgame, zeronormalizedcheck
Examples
v <- c(0, 0, 0, 1, 1, 1, 2)
zeromonotoniccheck(v, binary = TRUE)
monotoniccheck(v, binary = TRUE)
w <- c(-2,-2,-2,7,7,7,6)
zeromonotoniccheck(w)
monotoniccheck(w)
z <- c(1, 1, 1, 2, 2, 2, 2)
zeromonotoniccheck(z)
monotoniccheck(z)
[Package TUGLab version 0.0.1 Index]