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multilinear extension.

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Separability by semivalues modified for games with coalition structure
Rafael Amer, José Miguel Giménez
Journal:

RAIRO - Operations Research / Volume 43 / Issue 2 / April 2009

Published online by Cambridge University Press:

28 April 2009, pp. 215-230

Print publication:

April 2009
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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.