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Decisions in Economics and Finance

, Volume 41, Issue 2, pp 489–529 | Cite as

Proper strong-Fibonacci games

  • Flavio Pressacco
  • Laura ZianiEmail author
Article
  • 68 Downloads

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 \({\varPhi }\).

Keywords

Weighted majority games Natural representation Homogeneous representation Profile vector Fibonacci numbers Golden ratio 

JEL Classification

C71 

Notes

Acknowledgements

We wish to thank the editor and three anonymous reviewers for their helpful comments and suggestions.

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Copyright information

© Associazione per la Matematica Applicata alle Scienze Economiche e Sociali (AMASES) 2018

Authors and Affiliations

  1. 1.Department of Economics and Statistics D.I.E.S.Udine UniversityUdineItaly

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