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A Stability Index for Local Effectivity Functions

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Author Info
Joseph Abdou () (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)

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Abstract

We study the structure of unstable local effectivity functions defined for n players and p alternatives. A stability index based on the notion of cycle is introduced. In the particular case of simple games, the stability index is closely related to the Nakamura Number. In general it may be any integer between 2 and p. We prove that the stability index for maximal effectivity functions and for maximal local effectivity functions is either 2 or 3.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00331223_v1.

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Date of creation: Jul 2008
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Handle: RePEc:hal:cesptp:halshs-00331223_v1

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Related research
Keywords: Effectivity function; local effectivity function; acyclicity; stability index; Nakamura Number; acyclicity.;

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  1. Joseph Abdou, 2009. "The Structure of Unstable Power Systems," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00389181_v1, HAL. [Downloadable!]
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