Modification of Semivalues for Games with Coalition Structures |
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| Authors: | Rafael Amer José Miguel giménez |
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| Institution: | (1) Department of Applied Mathematics II and Industrial Engineering School of Terrassa, Polytechnic University of Catalonia, Colom 11, E-08222 Terrassa, Spain; Fax;(2) José Miguel Giménez, Department of Applied Mathematics III and Polytechnic School of Manresa, Polytechnic University of Catalonia, Bases de Manresa 61, E-08240 Manresa, Spain |
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| Abstract: | Consideration of reference systems for semivalues leads us to a global representation of the action of a semivalue on a game. Using this representation, we show how to modify semivalues to take account of coalition structures on the player set. The players' allocations according to a semivalue, including a modified semivalue, can be computed by means of products of matrices obtained from the multilinear extension of the game. |
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| Keywords: | Coalition structure Cooperative game Multilinear extension Semivalue |
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