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, Volume 26, Issue 1, pp 164–186 | Cite as

A note on multinomial probabilistic values

Original Paper

Abstract

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.

Keywords

Game theory Cooperative game Shapley value Probabilistic value Binomial semivalue 

Mathematics Subject Classification

91A12 

Notes

Acknowledgements

The authors wish to thank two anonymous reviewers for their helpful comments.

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Copyright information

© Sociedad de Estadística e Investigación Operativa 2017

Authors and Affiliations

  1. 1.Department of Mathematics, School of Industrial, Aerospace and Audiovisual Engineering of TerrassaUniversitat Politècnica de Catalunya (UPC)BarcelonaSpain
  2. 2.Department of Mathematics, Engineering School of ManresaUniversitat Politècnica de Catalunya (UPC)BarcelonaSpain

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