monotoniccheck {TUGLab}R Documentation

Monotonic check

Description

This function checks if the given game is monotonic.

Usage

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

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 monotonic if v(S) \le v(T) for all S, T \in 2^N such that S\subset T.

Value

TRUE if the game is monotonic, FALSE otherwise. If instance=TRUE and the game is not monotonic, the function also returns the positions (binary order positions if binary=TRUE; lexicographic order positions otherwise) of a pair of coalitions violating monotonicity.

See Also

additivecheck, superadditivecheck, zeromonotoniccheck

Examples

v <- c(0, 0, 1, 5, 1, 1, 2)
monotoniccheck(v, binary=FALSE, instance=TRUE)

[Package TUGLab version 0.0.1 Index]