belongsToCoreCover {CoopGame}

Check if point is core cover element

Description

belongsToCoreCover checks if the point is in the core cover

Usage

belongsToCoreCover(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 core cover, FALSE otherwise

Author(s)

Johannes Anwander [e-mail]

Jochen Staudacher [e-mail]

References

Tijs S.H. and Lipperts F.A.S. (1982) "The hypercube and the core cover of n-person cooperative games", Cahiers du Centre d' Etudes de Researche Operationelle 24, pp. 27–37

Branzei R., Dimitrov D. and Tijs S. (2006) Models in cooperative game theory, Springer, p. 21

Chakravarty S.R., Mitra M. and Sarkar P. (2015) A Course on Cooperative Game Theory, Cambridge University Press, pp. 45–46

Examples

library(CoopGame)
belongsToCoreCover(x=c(1,1,1), v=c(0,0,0,1,1,1,3))


library(CoopGame)
v <- c(0,0,0,3,3,3,6)
belongsToCoreCover(x=c(2,2,2),v)
#[1] TRUE
belongsToCoreCover(x=c(1,2,4),v)
#[1] FALSE