Given a game, this function computes its \(\tau\)-value.
Usage
tauvalue(v, binary = FALSE)
Value
The \(\tau\)-value of the game, as a 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
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 \(\sum_{i\in N}\tau_i(v)=v(N)\).
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).
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