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

In this paper we show a new method for calculating the nucleolus by solving a unique minimization linear program with 0(4(n)) constraints whose coefficients belong to {-1,0, 1}. We discuss the need of having all these constraints and empirically prove that they can be reduced to O(k(max)2(n)), where k(max) 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. (C) 2013 Elsevier Ltd. All rights reserved.