 Stability Index of Interaction formsUniversité Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL 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. Keywords: Interactive Form; Stability Index; Nash Equilibrium; Strong Equilibrium; Solvability; Consistency; Simple Game; Effectivity Function; Acyclicity; Nakamura Number.; Nakamura Number (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:halshs-00347438 Access Statistics for this paper More papers in Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL |
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