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On the Computation of Weighted Shapley Values for Cooperative TU Games

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On the Computation of Weighted Shapley Values for Cooperative TU Games

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dc.contributor.author Dragan, Irinel C. en
dc.date.accessioned 2010-06-03T18:15:07Z en
dc.date.available 2010-06-03T18:15:07Z en
dc.date.issued 2008 en
dc.identifier.uri http://hdl.handle.net/10106/2338 en
dc.description.abstract This paper is considering the problem of dividing fairly the worth of the grand coalition in a transferable utilities game, in case that the coalition is formed. The computational experience for the Shapley Value, the most famous solution, is extensive, but the case of the Weighted Shapley Value and that of the Kalai-Samet Value have been barely considered. Based upon some results connected to the null space of the first of these last two operators, an algorithm for computing the Weighted Shapley Value is developed. The case of the Kalai-Samet Value, a more general value, that is reducible to a vector of weighted values, is also considered. A nice new algorithm to be used for the particular case of the Shapley Value, is derived from the Weighted Shapley Value algorithm. Examples are illustrating the stated algorithms applied to all cases. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;360 en
dc.subject Shapley value en
dc.subject Weighted shapley value en
dc.subject Kalai-Samet value en
dc.subject Null space of a linear operator en
dc.subject.lcsh Mathematics Research en
dc.subject.lcsh Game theory en
dc.title On the Computation of Weighted Shapley Values for Cooperative TU Games en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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