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

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)...

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Bibliographic Details
Published in:Economics letters 2019-06, Vol.179, p.49-52
Main Author: Pham, Ngoc Anh
Format: Article
Language:English
Subjects:
Cost analysis
Cost sharing
Cost-sharing problem
Equality
Inequality
Lorenz comparison
Lorenz Curve
Serial cost sharing
Shapley value
Technology
Trade surplus
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Summary: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. •When the cost is concave, Increasing serial cost shares is Lorenz dominating.•When the cost function is convex, the Shapley value is Lorenz dominating.•A complete Lorenz ordering among four popular cost sharing rule can be obtained.
ISSN:0165-1765
1873-7374
DOI:10.1016/j.econlet.2019.03.015