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Graph-Restricted Games with Coalition Structures Anna B. Khmelnitskaya

Summary: Graph-Restricted Games with Coalition Structures
Anna B. Khmelnitskaya
SPb Institute for Economics and Mathematics Russian Academy of Sciences,
1 Tchaikovsky St., 191187 St.Petersburg, Russia
E-mail: a.khmelnitskaya@math.utwente.nl
Abstract We consider a new model of a TU game endowed with both coali-
tion and two-level cooperation structures that applies to various network sit-
uations. The approach to the value is close to that of both Myerson (1977)
and Aumann and Dr`eze (1974): it is based on ideas of component efficiency
and of one or another deletion link property, and it treats an a priori union
as a self-contained unit; moreover, our approach incorporates also the idea
of the Owen's quotient game property (1977). The axiomatically introduced
values possess an explicit formula representation and in many cases can be
quite simply computed. The results obtained are applied to the problem of
sharing an international river among multiple users without international
Keywords: TU game, coalition structure, cooperation structure, Myerson
value, Owen value, Aumann-Dr`eze value, component efficiency, deletion link
Mathematics Subject Classification (2000): 91A12, 91A40, 91A43


Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente


Collections: Engineering