Priority Parsimonious Games form a new subclass of Isbell’s classical Parsimonious Games and link their structure to Horadam’s generalized Fibonacci sequences. For each N > 3, we show that there exist exactly N − 3 distinct PPGs with N non-dummy players, each determined by a priority condition on the binary representation. For this class, we derive in closed form the profile, the type weights, and the winning quota. These quantities are organized through a Magic Table, which encodes one-step delayed generalized Fibonacci sequences and provides a unified representation of the whole PPG family.
When games follow Fibonacci: from Isbell’s construction to priority parsimonious games via Horadam sequences
Laura Ziani
Primo
Writing – Review & Editing
2026-01-01
Abstract
Priority Parsimonious Games form a new subclass of Isbell’s classical Parsimonious Games and link their structure to Horadam’s generalized Fibonacci sequences. For each N > 3, we show that there exist exactly N − 3 distinct PPGs with N non-dummy players, each determined by a priority condition on the binary representation. For this class, we derive in closed form the profile, the type weights, and the winning quota. These quantities are organized through a Magic Table, which encodes one-step delayed generalized Fibonacci sequences and provides a unified representation of the whole PPG family.File in questo prodotto:
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