Computing the NTU-Shapley value of NTU-games defined by multiple objectivelinear programs

In this paper we study a class of cooperative games with nontransferable ut ility (NTU) derived from multiple objective linear-programs (MOLP's). This is done in order to introduce the NTU-Shapley value as a solution to multip le objective linear programming. We present an algorithm for the computation of the set of all NTU-Shapley v alues for the bicriterion cases, which is based on:the simplex algorithm. F urthermore, we give a new optimal recursive procedure for the computation o f the Shapley value of TU-games.