Volume 43, Number 2, April-June 2009
|Page(s)||215 - 230|
|Published online||28 April 2009|
Separability by semivalues modified for games with coalition structure
Department of Applied
Mathematics II and Industrial and Aeronautic Engineering School of
Terrassa, Technical University of Catalonia, Spain. email@example.com
2 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. firstname.lastname@example.org
Accepted: 6 March 2009
Two games are inseparable by semivalues if both games obtain the same allocation whatever semivalue is considered. The problem of separability by semivalues reduces to separability from the null game. For four or more players, the vector subspace of games inseparable from the null game by semivalues contains games different to zero-game. Now, for five or more players, the consideration of a priori coalition blocks in the player set allows us to reduce in a significant way the dimension of the vector subspace of games inseparable from the null game. For these subspaces we provide basis formed by games of a particular type.
Mathematics Subject Classification: 91A12 / 91A70
Key words: Cooperative games / semivalue / semivalue modified for games with coalition structure / separability / multilinear extension.
© EDP Sciences, ROADEF, SMAI, 2009
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