TUGLab (version 0.0.1)

zeronormalizedgame: 0-normalized game

Description

Given a game, this function returns the characteristic function of its 0-normalization.

Usage

zeronormalizedgame(v, binary = FALSE)

Value

The characteristic function of the 0-normalized game, as a vector in binary order if binary=TRUE and in lexicographic order otherwise.

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.

Details

The 0-normalization of a given \(v\in G^N\) is defined by \(v_0(S)=v(S)-\sum_{i\in S} v(i)\) for each \(S \in 2^N\).

See Also

normalizedgame, savingsgame, strategicallyequivalentcheck, zeromonotoniccheck, zeronormalizedcheck

Examples

zeronormalizedgame(c(0,3,7,15,17,27,30))
zeronormalizedgame(c(1,5,10,6,11,15,16))
v.random <- rnorm(2^5-1,58,13)
zeronormalizedgame(v.random) == -savingsgame(v.random)