ABSTRACT

We consider a situation when a group of agents must be served in a facility. The facility can serve one agent at a time and agents incur waiting costs. The queueing problem is concerned with finding the order in which to serve agents and the (positive or negative) monetary transfers they should receive. In this chapter, we give a survey on the literature which tries to solve the queueing problem by applying the Shapley value after appropriately defining the worth of a coalition. For the queueing problem without an initial queue, the worth of a coalition can be defined to be the minimum waiting costs incurred by its members under either the optimistic assumption that they are served before the non-coalitional members or the pessimistic assumption that they are served after the non-coalitional members. On the other hand, for the queueing problem with an initial queue, the worth of a coalition is defined to be the minimum waiting cost of the coalition after efficiently reordering theirpositions in the queue by themselves. We also discuss the properties of allocation rules obtained by applying the Shapley value.