The equivalence of uniform and Shapley value-based cost allocations in a specific game

This paper concerns the possible equivalence of the Shapley value and other allocations in specific games. For a group buying game with a linear quantity discount schedule, the uniform allocation results in the same cost allocation as the Shapley value. In this paper, we explore whether the Shapley axioms can be used to make such connections. We also characterize the functions that result in the equivalence of these two allocations among the class of polynomial total cost functions.