A Stability Index for Local Effectivity Functions

Joseph Abdou

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

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.

Keywords: Stability index; acyclicity; strong Nash Equilibrium; core; solvability; consistency; simple game; effectivity function; Indice de stabilité; fonction d'effectivité; jeu simple; cycle; coeur; nombre de Nakamura (search for similar items in EconPapers)
Date: 2009-01
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00392508v1
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Published in 2009

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Related works:
Journal Article: A stability index for local effectivity functions (2010)
Working Paper: A Stability Index for Local Effectivity Functions (2010)
Working Paper: A Stability Index for Local Effectivity Functions (2010)
Working Paper: A Stability Index for Local Effectivity Functions (2010)
Working Paper: A Stability Index for Local Effectivity Functions (2009)
Working Paper: A Stability Index for Local Effectivity Functions (2009)
Working Paper: A Stability Index for Local Effectivity Functions (2008)
Working Paper: A Stability Index for Local Effectivity Functions (2008)
Working Paper: A stability index for local effectivity functions (2008)
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