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Stability Index of Interaction forms

Author

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  • Joseph Abdou

    () (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne, PSE - Paris School of Economics)

Abstract

An interaction form is an abstract model of interaction based on a description of power distribution among agents over alternatives. A solution known as the settlement set is defined at any preference profile. Necessary and sufficient conditions for stability, that is the existence of settlements, are established. A Stability Index that plays a role similar to that of the Naka- mura Number is defined. It measures, loosely speaking, the complexity of those configurations that prevent a settlement. To any strategic game form one can associate an interaction form in such a way that given an equilibrium concept (e.g. Nash or strong Nash) and a preference profile, settlements of the interaction form are precisely the equilibrium outcomes of the resulting game. As a consequence we have necessary and sufficient conditions for the solvability of game forms. The paper provides a localization of the index in case of unstability.

Suggested Citation

  • Joseph Abdou, 2008. "Stability Index of Interaction forms," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00347438, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00347438
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00347438
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    Keywords

    Nakamura Number; Interactive Form; Stability Index; Nash Equilibrium; Strong Equilibrium; Solvability; Consistency; Simple Game; Effectivity Function; Acyclicity; Nakamura Number.;

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