When games follow Fibonacci from Isbell’s construction to priority parsimonious games via Horadam sequences

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 $$N>3$$ N > 3 , we show that there exist exactly $$N-3$$ N - 3 distinct PPGs with N 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.