A study of the nucleolus in the nested cost-sharing problem: Axiomatic and strategic perspectives

We investigate the nucleolus from both axiomatic and strategic perspectives in the nested cost-sharing problem in which the cost of a public facility has to be shared among agents having different needs for it. We adopt a Right-endpoint Subtraction (RS) formulation, which underlies these two propert...

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Bibliographic Details
Published in:Games and economic behavior 2018-05, Vol.109, p.82-98
Main Authors: Hu, Cheng-Cheng, Tsay, Min-Hung, Yeh, Chun-Hsien
Format: Article
Language:English
Subjects:
Airport problem
Axiomatization
Consistency
Nash program
Nucleolus
Strategic justification
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Summary:We investigate the nucleolus from both axiomatic and strategic perspectives in the nested cost-sharing problem in which the cost of a public facility has to be shared among agents having different needs for it. We adopt a Right-endpoint Subtraction (RS) formulation, which underlies these two properties: RS bilateral consistency and RS converse consistency. As we show, the nucleolus is the only RS bilaterally consistent (or RS conversely consistent) rule satisfying equal treatment of equals and last-agent cost additivity. In addition, we introduce a game exploiting the two properties to strategically justify the nucleolus. Our results, together with the axiomatization and strategic justification of the Constrained Equal Benefits (CEB) rule in Hu et al. (2012), show that adopting different formulations to define a reduced problem leads to axiomatizing and, in particular, strategically justifying the CEB rule and the nucleolus in the nested cost-sharing problem. •RS bilateral consistency and RS converse consistency are proposed.•Based on the properties, the nucleolus is axiomatized.•A three-stage extensive form game exploiting the properties implements the nucleolus.•Different formulations of a reduced problem lead to implement different rules.
ISSN:0899-8256
1090-2473
DOI:10.1016/j.geb.2017.11.012