On the Coincidence of the Shapley Value and the Nucleolus in Queueing Problems

Given a group of agents to be served in a facility, the queueing problem is concerned with finding the order to serve agents and the (positive or negative) monetary compensations they should receive. As shown in Maniquet (2003), the minimal transfer rule coincides with the Shapley value of the game obtained by defining the worth of each coalition to be the minimum total waiting cost incurred by its members under the assumption that they are served before the non-coalitional members. Here, we show that it coincides with the nucleolus of the same game. Thereby, we establish the coincidence of the Shapley value and the nucleolus for queueing problems. We also investigate the relations between the minimal transfer rule and other rules discussed in the literature.