TUGLab (version 0.0.1)

zeromonotoniccheck: 0-monotonic check

Description

This function checks if the given game is 0-monotonic.

Usage

zeromonotoniccheck(v, binary = FALSE, instance = FALSE)

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.

Arguments

v

A characteristic function, as a vector.

binary

A logical value. By default, binary=FALSE. Should be set to TRUE if v is introduced in binary order instead of lexicographic order.

instance

A logical value. By default, instance=FALSE.

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 \(v\).

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)