On cooperative games, inseparable by semivalues

R. Amer*, J. Derks, J. Giménez

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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.
Original languageEnglish
Pages (from-to)181-188
Number of pages8
JournalInternational Journal of Game Theory
Publication statusPublished - 2003

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