Nucleolus {GameTheory}

Nucleolus solution

Description

This function computes the nucleolus solution of a game with a maximum of 4 agents.

Usage

Nucleolus(x, type = "Gains")

Arguments

x

Object of class Game

type

Specify if the game refers to Gains or Cost

Details

The nucleolus looks for an individually rational distribution of the worth of the grand coalition in which the maximum dissatisfaction is minimized. The nucleolus selects the element in the core, if this is nonempty, that lexicographically minimizes the vector of non-increasing ordered excesses of coalitions. In order to compute this solution we consider a sequence of linear programs, which looks for an imputation that minimizes the maximum excess among all coalitions.

Value

The command returns a table with the following elements:

v(S)

Individual value of player i

x(S)

Nucleolus solution of the player i

Ei

Excess of the player i

Author(s)

Sebastian Cano-Berlanga <[e-mail]>

References

Lemaire J (1991). "Cooperative game theory and its insurance applications." Astin Bulletin, 21(01), 17–40.

Schmeidler D (1969). "The Nucleolus of a characteristic function game." SIAM Journal of Applied Mathematics, 17, pp.1163–1170.

Examples

	
## EXAMPLE FROM LEMAIRE (1991)
	
# Begin defining the game

COALITIONS <- c(46125,17437.5,5812.5,69187.5,53812.5,30750,90000)
LEMAIRE<-DefineGame(3,COALITIONS)

# End defining the game

LEMAIRENUCLEOLUS<-Nucleolus(LEMAIRE)
summary(LEMAIRENUCLEOLUS) # Gains Game, the excess should be negative