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Disentangle the Florentine Families Network by the Pre-Kernel

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  • Meinhardt, Holger Ingmar

Abstract

For different model settings we conduct power analyses on the Florentine families network of the 15th century while referring to the most popular power indices like the Shapley-Shubik or Banzhaf value as well as to the pre-nucleolus and pre-kernel. In order to assess their capacity to identify the main protagonists that correspond with the chronicles, we inspect of how the power distributions are spread around the mean. Distributions that are clustered to close around the mean cannot identify outstanding positions. In this respect, they failed to provide a scenario that corresponds with the annals. As it turns out, the pre-kernel solution – as a solution concept designed for studying bargaining situations – retrieves the most accurate image for the examined network structures. Last but not least, we discovered two new non-homogeneous weighted majority games with a disconnected pre-kernel.

Suggested Citation

  • Meinhardt, Holger Ingmar, 2021. "Disentangle the Florentine Families Network by the Pre-Kernel," MPRA Paper 106482, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:106482
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    References listed on IDEAS

    as
    1. Meinhardt, Holger Ingmar, 2017. "Simplifying the Kohlberg Criterion on the Nucleolus: A Disproof by Oneself," MPRA Paper 77143, University Library of Munich, Germany.
    2. Dan S. Felsenthal, 2016. "Erratum to: A Well-Behaved Index of a Priori P-Power for Simple N-Person Games," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 33(4), pages 383-383, December.
    3. Axel Ostmann & Holger Meinhardt, 2007. "Non-binding agreements and fairness in commons dilemma games," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 15(1), pages 63-96, March.
    4. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    6. Xiaotie Deng & Christos H. Papadimitriou, 1994. "On the Complexity of Cooperative Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 19(2), pages 257-266, May.
    7. Meinhardt, Holger Ingmar, 2020. "On the Replication of the Pre-Kernel and Related Solutions," MPRA Paper 102676, University Library of Munich, Germany.
    8. Bozzo, Enrico & Franceschet, Massimo & Rinaldi, Franca, 2015. "Vulnerability and power on networks," Network Science, Cambridge University Press, vol. 3(2), pages 196-226, June.
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    10. Meinhardt, Holger Ingmar, 2014. "A Note on the Computation of the Pre-Kernel for Permutation Games," MPRA Paper 59365, University Library of Munich, Germany.
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    More about this item

    Keywords

    Transferable Utility Game; (Non-)Homogeneous Game; Disconnected Pre-Kernel; Convex Analysis; Fenchel-Moreau Conjugation; Pre-Nucleolus; Shapley-Shubik Index; Banzhaf Value; Deegan-Packel Index; Johnston Index; Public Good Index.;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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