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A Strategic Implementation of the Shapley Value for the Nested Cost‐Sharing Problem
Author(s) -
CHUN YOUNGSUB,
HU CHENGCHENG,
YEH CHUNHSIEN
Publication year - 2017
Publication title -
journal of public economic theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.809
H-Index - 32
eISSN - 1467-9779
pISSN - 1097-3923
DOI - 10.1111/jpet.12190
Subject(s) - shapley value , subgame perfect equilibrium , rationality , cost sharing , cooperative game theory , outcome (game theory) , class (philosophy) , value (mathematics) , microeconomics , mathematical economics , economics , game theory , computer science , political science , law , artificial intelligence , machine learning
When agents have different needs for a public facility but serving a given agent allows serving all agents with smaller needs than his without any extra cost, how should the agents divide the cost of the facility among themselves? We provide a strategic implementation of the Shapley value for this class of cost‐sharing problems. We introduce a three‐stage extensive form game that respects individual rationality and show that there is one and only one subgame‐perfect equilibrium outcome of the game. Moreover, it is the allocation assigned by the Shapley value.