CoopGame (version 0.2.2)

belongsToReasonableSet: Check if point is element of reasonable set

Description

belongsToReasonableSet checks if the point is in the reasonable set

Usage

belongsToReasonableSet(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 reasonable set, FALSE otherwise

References

Milnor J.W. (1953) Reasonable Outcomes for N-person Games, Rand Corporation, Research Memorandum RM 916.

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. 43--44

Gerard-Varet L.A. and Zamir S. (1987) "Remarks on the reasonable set of outcomes in a general coalition function form game", Int. Journal of Game Theory 16(2), pp. 123--143

Examples

# NOT RUN {
library(CoopGame)
belongsToReasonableSet(x=c(1,0.5,0.5), v=c(0,0,0,1,1,1,2))

# }
# NOT RUN {
library(CoopGame)
v <- c(0,0,0,3,3,3,6)
belongsToReasonableSet(x=c(2,2,2),v)
#[1] TRUE
belongsToReasonableSet(x=c(1,2,4),v)
#[1] FALSE
# }