Proper strong-Fibonacci games

Autor: Laura Ziani, Flavio Pressacco
Jazyk: angličtina
Rok vydání: 2018
Předmět:
Popis: We define proper strong-Fibonacci (PSF) games as the subset of proper homogeneous weighted majority games which admit a Fibonacci representation. This is a homogeneous, type-preserving representation whose ordered sequence of type weights and winning quota is the initial string of Fibonacci numbers of the one-step delayed Fibonacci sequence. We show that for a PSF game, the Fibonacci representation coincides with the natural representation of the game. A characterization of PSF games is given in terms of their profile. This opens the way up to a straightforward formula which gives the number $$\varPsi (t)$$ of such games as a function of t, number of non-dummy players’ types. It turns out that the growth rate of $$\varPsi (t)$$ is exponential. The main result of our paper is that, for two consecutive t values of the same parity, the ratio $$\varPsi (t+2)/\varPsi (t)$$ converges toward the golden ratio $${\varPhi }$$ .
Databáze: OpenAIRE
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