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Proper strong-Fibonacci games

Pressacco, Flavio
•
Ziani, Laura
2018
  • journal article

Periodico
DECISIONS IN ECONOMICS AND FINANCE
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 Ψ(t) of such games as a function of t, number of non-dummy players’ types. It turns out that the growth rate of Ψ(t) is exponential. The main result of our paper is that, for two consecutive t values of the same parity, the ratio Ψ(t + 2)/Ψ (t) converges toward the golden ratio Φ.
DOI
10.1007/s10203-018-0212-5
WOS
WOS:000454246200020
Archivio
http://hdl.handle.net/11390/1143793
info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-85053454840
Diritti
open access
Soggetti
  • Fibonacci number

  • Golden ratio

  • Homogeneous represent...

  • Natural representatio...

  • Profile vector

  • Weighted majority gam...

  • Finance

  • Economics, Econometri...

Scopus© citazioni
0
Data di acquisizione
Jun 7, 2022
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Web of Science© citazioni
0
Data di acquisizione
Mar 21, 2024
Visualizzazioni
1
Data di acquisizione
Apr 19, 2024
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