TUGLab (version 0.0.1)

minimalrightsvector: Minimal rights vector

Description

This function computes the minimal rights vector of a game.

Usage

minimalrightsvector(v, binary = FALSE)

Value

The minimal rights vector.

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

Given \(v\in G^N\), the utopia payoff of player \(i\in N\) is defined as \(M_i(N,v)=v(N)-v(N\backslash i)\).

The minimal right of player \(i\in N\) is defined as \(m_i(N,v)=\max_{S:i\in S}(v(S)-\sum_{j\in S\backslash i}M_j(N,v))\).

See Also

utopiapayoffsvector

Examples

v <- c(0, 0, 0, 1, 1, 1, 2)
minimalrightsvector(v)
convexcheck(v)
minimalrightsvector(v) == c(v[1],v[2],v[3])
w <- c(0,0,0,4,7,6,10)
convexcheck(w)
minimalrightsvector(w) == c(w[1],w[2],w[3])