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A note on multinomial probabilistic values

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  • Francesc Carreras

    (Universitat Politècnica de Catalunya (UPC))

  • María Albina Puente

    (Universitat Politècnica de Catalunya (UPC))

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.

Suggested Citation

  • Francesc Carreras & María Albina Puente, 2018. "A note on multinomial probabilistic values," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 164-186, April.
    • Handle: RePEc:spr:topjnl:v:26:y:2018:i:1:d:10.1007_s11750-017-0464-1
    DOI: 10.1007/s11750-017-0464-1
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    References listed on IDEAS

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    1. Pradeep Dubey & Abraham Neyman & Robert James Weber, 1981. "Value Theory Without Efficiency," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 122-128, February.
    2. Carreras, Francesc, 2005. "A decisiveness index for simple games," European Journal of Operational Research, Elsevier, vol. 163(2), pages 370-387, June.
    3. Josep Freixas & Montserrat Pons, 2015. "An axiomatic characterization of the potential decisiveness index," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(3), pages 353-359, March.
    4. Feltkamp, Vincent, 1995. "Alternative Axiomatic Characterizations of the Shapley and Banzhaf Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(2), pages 179-186.
    5. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    6. Josep Freixas & M. Puente, 2002. "Reliability Importance Measures of the Components in a System Based on Semivalues and Probabilistic Values," Annals of Operations Research, Springer, vol. 109(1), pages 331-342, January.
    7. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
    8. Rafael Amer & José Miguel giménez, 2003. "Modification of Semivalues for Games with Coalition Structures," Theory and Decision, Springer, vol. 54(3), pages 185-205, May.
    9. Francesc Carreras & María Albina Puente, 2012. "Symmetric Coalitional Binomial Semivalues," Group Decision and Negotiation, Springer, vol. 21(5), pages 637-662, September.
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    Cited by:

    1. Francesc Carreras & María Albina Puente, 2022. "On the axiomatic characterization of the coalitional multinomial probabilistic values," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 119-151, April.
    2. Benati, Stefano & López-Blázquez, Fernando & Puerto, Justo, 2019. "A stochastic approach to approximate values in cooperative games," European Journal of Operational Research, Elsevier, vol. 279(1), pages 93-106.

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