tauvalue {TUGLab}R Documentation

\tau-value

Description

Given a game, this function computes its \tau-value.

Usage

tauvalue(v, binary = 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.

Details

The \tau-value of v\in G^N is given by

\tau(v)=m(v)+\alpha (M(v)-m(v)),

where M(v) is the vector of utopia payoffs, m(v) is the vector of minimal rights, and \alpha is the value for which \sum_{i\in N}\tau_i(v)=v(N).

Value

The \tau-value of the game, as a vector.

References

Tijs, S. H. (1981). Bounds for the core of a game and the \tau-value. In O. Moeschlin and D. Pallaschke (Eds.), Game theory and mathematical economics (pp. 123-132).

See Also

minimalrightsvector, utopiapayoffsvector.

Examples

tauvalue(c(0,0,0,0,10,40,30,60,10,20,90,90,90,130,160))

# What if the game is a cost game?
cost.v <- c(2,2,2,3,4,4,5) # cost game
-tauvalue(-cost.v) # tau-value of the cost game

[Package TUGLab version 0.0.1 Index]