A Stability Index for Local Effectivity Functions
AbstractWe 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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Bibliographic InfoPaper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number 09041.
Length: 22 pages
Date of creation: Jan 2009
Date of revision: Oct 2009
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Stability index; acyclicity; strong Nash equilibrium; core; solvability; consistency; simple game; effectivity function.;
Other versions of this item:
- Joseph Abdou, 2008. "A stability index for local effectivity functions," Documents de travail du Centre d'Economie de la Sorbonne b08056, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
- C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
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- repec:hal:wpaper:halshs-00633589 is not listed on IDEAS
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