Proper strong-Fibonacci games |
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Authors: | Flavio Pressacco Laura Ziani |
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Affiliation: | 1.Department of Economics and Statistics D.I.E.S.,Udine University,Udine,Italy |
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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 }). |
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