nucleolus {GameTheoryAllocation}

Nucleolus

Description

This function gives the nucleolus described in Schmeidler (1969).

Usage

nucleolus(characteristic_function, game = c("profit", "cost"))

Arguments

characteristic_function

A vector with the characteristic function v(S) (or c(S), if we work with a cost game), according to the order of coalitions shown in coalitions function.

game

Characters to indicate if the game is a cost or profit game. The possibles values are "cost" or "profit".

Value

A vector with the allocation that nucleolus proposes.

Author(s)

A. Saavedra-Nieves

References

Schmeidler, D. (1969). The nucleolus of a characteristic function game, SIAM Journal of Applied Mathematics, vol. 17, pp. 1163-1170.

Examples

characteristic_function<-c(0,0.538, 0.761, 1.742, 0.554, 0.137, 0.293, 0.343)
nucleolus(characteristic_function,game="cost")
#[1] "Nucleolus"
#      1     2 3
#  0.137 0.206 0