Disentangle the Florentine Families Network by the Pre-Kernel

Meinhardt, Holger Ingmar (2021): Disentangle the Florentine Families Network by the Pre-Kernel.

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.

• Item Type: MPRA Paper
• Language: English
• 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.
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games

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