On the nucleolus of NTU-games defined by multiple objective linear programs

In this article the authors derive a class of cooperative games with non-transferable utility from multiple objective linear programs. This is done in order to introduce the nucleolus, a solution concept from cooperative game theory, as a solution to multiple objective linear problems. The authors show that the nucleolus of such a game is a singleton, which is characterized by inclusion in the least core and the reduced game property. Furthermore the nucleolus satisfies efficiency, anonymity and strategic equivalence. The authors also present a polynomially bounded algorithm for computation of the nucleolus. Let n be the number of objective functions. The nucleolus is obtained by solving at most 2n linear programs. Initially the ideal point is computed by solving n linear programs. Then a sequence of at most n linear programs is solved, and the nucleolus is obtained as the unique solution of the last program.