Proper strong-Fibonacci games
Autor: | Laura Ziani, Flavio Pressacco |
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Jazyk: | angličtina |
Rok vydání: | 2018 |
Předmět: |
Fibonacci number
Economics Natural representation Homogeneous representation Fibonacci numbers Weighted majority games Exponential function Econometrics and Finance (all)2001 Economics Combinatorics Golden ratio Profile vector Finance Economics Econometrics and Finance (all)2001 Economics Econometrics and Finance (miscellaneous) Homogeneous Econometrics and Finance (miscellaneous) Parity (mathematics) General Economics Econometrics and Finance Mathematics |
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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