A pessimistic approach to the queueing problem

Given a group of agents to be served in a facility, the queueing problem is concerned with finding the order in which to serve agents and the (positive or negative) monetary compensations they should receive. Maniquet [F. Maniquet, A characterization of the Shapley value in queueing problems, Journal of Economic Theory 109 (2003), 90–103.] shows that the problem can be solved by applying the Shapley value to the game obtained by defining the worth of each coalition to be the minimum waiting cost incurred by its members under the assumption that they are served before the non-coalitional members. Here, we investigate a pessimistic definition for the worth of a coalition. It is obtained by assuming that the coalitional members are served after the non-coalitional members. Even though we apply the same value to the game, the resulting rule is very different from Maniquet's. We develop axiomatic characterizations of the rule.