This function checks if the given game is totally balanced and computes its totally balanced cover.
Usage
totallybalancedcheck(
v,
game = FALSE,
binary = FALSE,
tol = 100 * .Machine$double.eps
)
Value
TRUE if the game is totally balanced, FALSE otherwise. If game=TRUE, the totally balanced cover of the game is also returned.
Arguments
v
A characteristic function, as a vector.
game
A logical value. By default, game=FALSE. If set to TRUE, the totally balanced cover of the game is also returned.
binary
A logical value. By default, binary=FALSE. Should be set to TRUE if v is introduced in binary order instead of lexicographic order.
tol
A tolerance parameter, as a non-negative number.
By default, tol=100*.Machine$double.eps.
Details
A game \(v \in G^{N}\) is totally balanced if all of its subgames are balanced
(the subgame of each coalition \(S \in 2^{N}\) with respect to \(v\) is defined by
\(v_S(T)=v(T)\) for all \(T\in 2^S\)).
References
Maschler, M., Solan, E., & Zamir, S. (2013). Game Theory. Cambridge University Press.