Cooperative Game Theoretic Approach

The queueing problem can be solved by applying solutions developed in cooperative game theory. To do so, queueing problems should be mapped into queueing games by defining a worth of coalition. We can define the worth of each coalition to be the minimum waiting cost incurred by its members under the optimistic assumption that they are served before the non-coalitional members. By applying the Shapley value to the optimistic queueing game, we obtain the minimal transfer rule. Alternatively, we can define the worth of each coalition to be the minimum total waiting cost incurred by its members under the pessimistic assumption that they are served after the non-coalitional members. If we apply the Shapley value to the pessimistic queueing game, we end up with a different rule, the maximal transfer rule. Next, we investigate what recommendations we have if other cooperative game theoretic solutions are applied to the queueing games. Surprisingly, we end up with the same recommendation: the Shapley value, the nucleolus (or the prenucleolus), and the τ-value coincide for queueing games.