On The Inverse Problem for Semivalues of Cooperative TU Games

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On The Inverse Problem for Semivalues of Cooperative TU Games

Show simple item record Dragan, Irinel C. en 2010-06-03T18:23:29Z en 2010-06-03T18:23:29Z en 2002-04 en
dc.identifier.uri en
dc.description.abstract In the present paper, we define a basis of [see pdf for notation] relative to a Semivalue, we compute the potentials of the subgames of a given game, to show that the basis is a potential basis, from which we get the Semivalues of the basic vectors. In this way we discover a basis of the null space of a Semivalue and derive, as in the previous work, a solution of the inverse problem, this time for a Semivalue. As the Shapley value was considered in detail in the previous work, we give a complete description for the Banzhaf value. As a byproduct of the results on the potential basis relative to a Semivalue, we give an algorithm for the computation of a Semivalue, called a dynamic algorithm, because the algorithm is building a finite sequence of games, with the same Semivalue as the given one, where the last game is providing the Semivalue by an easy computation. A similar algorithm for computing the Shapley value has been developed by M.Maschler (1982). We show also an accelerated algorithm which solves the problem in n steps. The case of a general three person cooperative TU game is shown for illustrating the concepts introduced, and a particular game is chosen to exhibit the application of the dynamic algorithm. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;348 en
dc.subject Semivalue en
dc.subject Cooperative game en
dc.subject TU games en
dc.subject Dynamic algorithm en
dc.subject Banzhaf value en
dc.subject Shapley value en
dc.subject.lcsh Mathematics Research en
dc.title On The Inverse Problem for Semivalues of Cooperative TU Games en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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