An Efficient Algorithm for Solving Nucleolus of Cooperative TU Games Using MATLAB

Abstract

The approach to determine the nucleolus of the cooperative game is to apply a sequence of linear programs. In this paper a new algorithm for solving Nucleolus for cooperative TU games is proposed.   Some constraints are dropped at any iteration for solving a linear program as those dropped constraints will not contribute in getting unique solution. Also dropping constraints will not affect in the single point Nucleolus solution but the total number of linear programs to be solved will be less in the proposed method. It can be claimed that Nucleolus can be obtained in solving maximum (n-1) linear programs for a n person cooperative TU games. Numerical examples for different set of players are provided. Advantages of using MATLAB are discussed. The results clearly prove the effectiveness of the proposed method with the usage of MATLAB.