K-Fibonacci sequences and minimal winning quota in Parsimonious game

Flavio Pressacco (), Giacomo Plazzotta and Laura Ziani ()
Additional contact information
Flavio Pressacco: DIES - DIES - Dept. of Economics and Statistics - Università degli Studi di Udine - University of Udine [Italie]
Giacomo Plazzotta: Department of Mathematics [Imperial College London] - Imperial College London
Laura Ziani: DIES - DIES - Dept. of Economics and Statistics - Università degli Studi di Udine - University of Udine [Italie]

Working Papers from HAL

Abstract: Parsimonious games are a subset of constant sum homogeneous weighted majority games unequivocally described by their free type representation vector. We show that the minimal winning quota of parsimonious games satisfies a second order, linear, homogeneous, finite difference equation with nonconstant coefficients except for uniform games. We provide the solution of such an equation which may be thought as the generalized version of the polynomial expansion of a proper k-Fibonacci sequence. In addition we show that the minimal winning quota is a symmetric function of the representation vector; exploiting this property it is straightforward to prove that twin Parsimonious games, i.e. a couple of games whose free type representations are each other symmetric, share the same minimal winning quota.

Keywords: Fibonacci polynomials; Homogeneous weighted majority games; parsimonious games; minimal winning quota; k-Fibonacci sequence; Fibonacci polynomials. (search for similar items in EconPapers)
Date: 2014-02-20
New Economics Papers: this item is included in nep-gth
Note: View the original document on HAL open archive server: https://hal.science/hal-00950090
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://hal.science/hal-00950090/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-00950090

Access Statistics for this paper

More papers in Working Papers from HAL
Bibliographic data for series maintained by CCSD ().