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Minimum Cut Tree Games

  • In this paper we introduce a cooperative game based on the minimum cut tree problem which is also known as multi-terminal maximum flow problem. Minimum cut tree games are shown to be totally balanced and a solution in their core can be obtained in polynomial time. This special core allocation is closely related to the solution of the original graph theoretical problem. We give an example showing that the game is not supermodular in general, however, it is for special cases and for some of those we give an explicit formula for the calculation of the Shapley value.

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Author:Anne M. Schwahn
URN (permanent link):urn:nbn:de:hbz:386-kluedo-15865
Serie (Series number):Report in Wirtschaftsmathematik (WIMA Report) (117)
Document Type:Report
Language of publication:English
Year of Completion:2008
Year of Publication:2008
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2008/12/19
Tag:Core; Kaktusgraph; Shapleywert; kooperative Spieltheorie; minimaler Schnittbaum
Shapley value; cactus graph; cooperative game; core; minimum cut tree
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011