TUGLab (version 0.0.1)

superadditivecheck: Superadditive check

Description

This function checks if the given game is superadditive.

Usage

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

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.

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 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.

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)