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

摘要

In this paper we show a new method for calculating the nucleolus by solving a unique minimization linear program with O(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.