Twin relationships in Parsimonious Games: some results

Flavio Pressacco (), Giacomo Plazzotta and Laura Ziani ()
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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]

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Abstract: In a vintage paper concerning Parsimonious games, a subset of constant sum homogeneous weighted majority games, Isbell introduced a twin relationship based on transposition properties of the incidence matrices upon minimal winning coalitions of such games. A careful investigation of such properties allowed the discovery of some results on twin games presented in this paper. In detail we show that a) twin games have the same minimal winning quota and b) each Parsimonious game admits a unique balanced lottery on minimal winning coalitions, whose probabilities are given by the individual weights of its twin game.

Keywords: balanced lottery; Homogeneous weighted majority games; incidence matrices; twin relationships; minimal winning quota; balanced lottery. (search for similar items in EconPapers)
Date: 2014-02-20
New Economics Papers: this item is included in nep-gth
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