Multinomial values were previously introduced by one of the authors in reliability and extended later to all cooperative games. Here, we present for this subfamily of probabilistic values three new results, previously stated only for binomial semivalues in the literature. They concern the dimension of the subspace spanned by the multinomial values and two characterizations: one, individual, for each multinomial value; another, collective, for the whole subfamily they form. Finally, an application to simple games is provided.
Game theory Cooperative game Shapley value Probabilistic value Binomial semivalue
Mathematics Subject Classification
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The authors wish to thank two anonymous reviewers for their helpful comments.
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