On cooperative games, inseparable by semivalues

On cooperative games, inseparable by semivalues

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Article ID: iaor20051899
Country: Germany
Volume: 32
Issue: 2
Start Page Number: 181
End Page Number: 188
Publication Date: Jan 2003
Journal: International Journal of Game Theory
Authors: , ,
Keywords: shuffle games
Abstract:

Semivalues like the Shapley value and the Banzhaf value may assign the same payoff vector to different games. It is even possible that two games attain the same outcome for all semivalues. Due to the linearity of the semivalues, this exactly occurs in case the difference of the two games is an element of the kernel of each semivalue. The intersection of these kernels is called the shared kernel, and its game theoretic importance is that two games can be evaluated differently by semivalues if and only if their difference is not a shared kernel element. The shared kernel is a linear subspace of games. The corresponding linear equality system is provided so that one is able to check membership. The shared kernel is spanned by specific {− 1, 0, 1}-valued games, referred to as shuffle games. We provide a basis with shuffle games, based on an a-priori given ordering of the players.

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