Lorenz comparison between Increasing serial and Shapley value cost-sharing rules

摘要

In this paper, we consider the cost (surplus) sharing problem when a coalition of agents operates under a common production technology and share the total cost (resp. output), given their individual demands (resp. input). We compare the allocation inequality between the Moulin-Shenker's (Increasing) serial and Shapley shares in the Lorenz sense, and show that Increasing serial share dominates the Shapley value when the marginal is decreasing, while the opposite is true when the marginal is increasing. Together with earlier comparisons between the two and the average shares, and the comparison between Increasing and Decreasing serial rules, the result implies a complete Lorenz ordering in equality among the four common sharing allocations: Average, Increasing serial, Decreasing serial and the Shapley value. (C) 2019 Elsevier B.V. All rights reserved.