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• W2891150178 abstract "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 $${varPhi }$$ ." @default.
• W2891150178 created "2018-09-27" @default.
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• W2891150178 date "2018-09-06" @default.
• W2891150178 modified "2023-10-18" @default.
• W2891150178 title "Proper strong-Fibonacci games" @default.
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• W2891150178 doi "https://doi.org/10.1007/s10203-018-0212-5" @default.
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