Issue RAIRO-Oper. Res. Volume 43, Number 2, April-June 2009 Page(s) 215 - 230 DOI 10.1051/ro/2009013 Published online 28 April 2009

RAIRO-Oper. Res. 43 (2009) 215-230
DOI: 10.1051/ro/2009013

Separability by semivalues modified for games with coalition structure

Rafael Amer¹ and José Miguel Giménez<sup>2

1</sup>  Department of Applied Mathematics II and Industrial and Aeronautic Engineering School of Terrassa, Technical University of Catalonia, Spain. rafel.amer@upc.edu
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. jose.miguel.gimenez@upc.edu

Received February 14, 2008. Accepted March 6, 2009. Published online 28 April 2009

Abstract
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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