Cooperative game theory: A note on an algorithm that has probably never been implemented

Some of the solution concepts within cooperative game theory suffer from the fact that they are difficult to compute. In this note, the authors study one of the solution concepts, the nucleolus. One algorithm from computing the nucleolus utilizes the fact that the dual of a certain linear programming problem is problem independent. Therefore, it can be solved ‘once and for all’ for every problem, of any size. However several numerical difficulties along with an extremely high computational complexity makes it practically impossible to implement the algorithm successfully. Some of the difficulties can be overcome, some cannot. A series of unfortunate circumstances make this algorithm part of a valuable lesson in practical numerical analysis-a less on that most people have to learn ‘the hard way’.