Finding the nucleolus of any n-person cooperative game by a single linear program

Abstract

In this paper we show a new method for calculating the nucleolus by solving a unique minimization linear program with O(4n) constraints whose coeffi- cients belong to {−1, 0, 1}. We discuss the need of having all these constraints and empirically prove that they can be reduced to O(kmax2 n), where kmax is a positive integer comparable with the number of players. A computational experience shows the applicability of our method over (pseudo)random transferable utility cooperative games with up to 18 players.