A fair staff allocation rule for the capacity pooling of multiple call centers

We construct a cooperative sta¢ ng game to investigate how to fairly allocate the reduced number of sta¤s among multiple call centers that pool (centralize) their capacities. We show that this game is essential and submodular, and thereby, convex with a non-empty core. We also propose a neat Shapley value-characterized sta¤-allocation rule, which exists in the core of the game.