belongsToWeberset {CoopGame}

Check if point is element of Weber Set

Description

belongsToWeberset checks if the point is in the Weber Set

Usage

belongsToWeberset(x, v)

Arguments

x

numeric vector containing allocations for each player

v

Numeric vector of length 2^n - 1 representing the values of the coalitions of a TU game with n players

Value

TRUE if point belongs to Weber Set and FALSE otherwise

Author(s)

Johannes Anwander [e-mail]

References

Weber R.J. (1988) "Probabilistic values for games". In: Roth A.E. (Ed.), The Shapley Value. Essays in in honor of Lloyd S. Shapley, Cambridge University Press, pp. 101–119

Peters H. (2015) Game Theory: A Multi-Leveled Approach, 2nd Edition, Springer, pp. 327–329

Examples

library(CoopGame)
belongsToWeberset(x=c(1,0.5,0.5), v=c(0,0,0,1,1,1,2))


library(CoopGame)
v=c(0,1,2,3,4,5,6)

#Point belongs to Weber Set:
belongsToWeberset(x=c(1.5,1,3.5),v)

#Point does not belong to Weber Set:
belongsToWeberset(x=c(2.05,2,2),v)