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Separability by semivalues modified for games with coalition structure

Published online by Cambridge University Press:  28 April 2009

Rafael Amer  and
José Miguel Giménez
Rafael Amer
Affiliation:
Department of Applied Mathematics II and Industrial and Aeronautic Engineering School of Terrassa, Technical University of Catalonia, Spain. [email protected]
José Miguel Giménez
Affiliation:
Department of Applied Mathematics III and Engineering School of Manresa, Technical University of Catalonia, Spain. Corresponding author. Mailing address: EPSEM, Avda. Bases de Manresa 61, 08242 Manresa, Spain. [email protected]
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Abstract

Two games are inseparable by semivalues if both gamesobtain the same allocation whatever semivalue is considered. The problem ofseparability by semivalues reduces to separability from the nullgame. For four or more players, the vector subspace of gamesinseparable from the null game by semivalues contains gamesdifferent to zero-game. Now, for five or more players, theconsideration of a priori coalition blocks in the player set allowsus to reduce in a significant way the dimension of the vectorsubspace of games inseparable from the null game. For thesesubspaces we provide basis formed by games of a particular type.

Keywords

Cooperative gamessemivaluesemivalue modified for games with coalition structureseparabilitymultilinear extension.
Type
Research Article
Information
RAIRO - Operations Research , Volume 43 , Issue 2 , April 2009 , pp. 215 - 230
Copyright
© EDP Sciences, ROADEF, SMAI, 2009

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References

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