Nucleolus | R Documentation |
This function computes the nucleolus solution of a game with a maximum of 4 agents.
Nucleolus(x, type = "Gains")
x |
Object of class Game |
type |
Specify if the game refers to Gains or Cost |
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.
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 |
Sebastian Cano-Berlanga <cano.berlanga@gmail.com>
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.
## 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
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