totallybalancedcheck {TUGLab}R Documentation

Totally balanced check

Description

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
)

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).

Value

TRUE if the game is totally balanced, FALSE otherwise. If game=TRUE, the totally balanced cover of the game is also returned.

References

Maschler, M., Solan, E., & Zamir, S. (2013). Game Theory. Cambridge University Press.

See Also

balancedcheck, subgame

Examples

totallybalancedcheck(c(0,0,0,0,1/2,0,0,1/2,0,1/2,1/2,1/2,1/2,1/2,1))
totallybalancedcheck(c(0,0,0,0,1,1,0,1,0,0,1,1,1,1,2),game=TRUE)

[Package TUGLab version 0.0.1 Index]