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Stability and Index of the Meet Game on a Lattice

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  • Joseph Abdou

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

Abstract

We study the stability and the stability index of the meet game form defined on a meet semilattice. Given any active coalition structure, we show that the stability index relative to the equilibrium, to the beta core and to the exact core is a function of the Nakamura number, the depth of the semilattice and its gap function.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00633589.

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Date of creation: Nov 2012
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Publication status: Published, International Journal of Game Theory, 2012, 41, 4, 775-789
Handle: RePEc:hal:cesptp:halshs-00633589

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Keywords: Effectivity Function; Lattice; Stability Index; Equilibrium; Nakamura Number;

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  1. Joseph Abdou, 2010. "A Stability Index for Local Effectivity Functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00389003, HAL.
  2. Peleg, Bezalel, 2002. "Game-theoretic analysis of voting in committees," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 8, pages 395-423 Elsevier.
  3. Moulin, Hervé & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Economics Papers from University Paris Dauphine 123456789/13220, Paris Dauphine University.
  4. Abdou, J., 2000. "Exact stability and its applications to strong solvability," Mathematical Social Sciences, Elsevier, vol. 39(3), pages 263-275, May.
  5. Joseph Abdou, 2012. "The structure of unstable power mechanisms," Economic Theory, Springer, vol. 50(2), pages 389-415, June.
  6. Abdou, Joseph & Keiding, Hans, 2003. "On necessary and sufficient conditions for solvability of game forms," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 243-260, December.
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