A Stability Index for Local Effectivity Functions

Joseph M. Abdou (1, 2)

1 PSE - Paris School of Economics
2 CES - Centre d'économie de la Sorbonne

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.

Mots clés: Stability Index; Acyclicity; Strong Nash Equilibrium; Core; Solvability; Consistency; Simple Game; Effectivity Function

Mots clés: Indice de stabilité; pouvoir; jeu simple; Coeur; cycle de Condorcet

Domaines: Science politique; Economies et finances

Joseph M. Abdou. A Stability Index for Local Effectivity Functions. Mathematical Social Sciences, 2010, 59 (3), pp.306-313. ⟨10.1016/j.mathsocsci.2009.12.003⟩. ⟨halshs-00389003⟩