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Interaction Sheaves on Continuous Domains

  • Joseph Abdou

    ()

    (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)

  • Hans Keiding

    (University of Copenhagen - University of Copenhagen)

We introduce a description of the power structure which is inherent in a strategic gameform using the concept of an interaction sheaf. The latter assigns to each open set of outcomes a set of interaction arrays, specifying the changes that coalitions can make if outcome belongs to this open set. The interaction sheaf generalizes the notion of effectivity functions which has been widely used in implementation theory, taking into consideration that changes in outcome may be sustained not only by single coalitions but possibly by several coalitions, depending on the underlying strategy choices. Also, it allows us to consider gameforms with not necessarily finite sets of outcomes, generalizing the results on solvability of game forms obtained in the finite case in Abdou and Keiding [Abdou, J., Keiding, H., 2003. On necessary and sufficient conditions for solvability of game forms. Mathematical Social Sciences 46, 243-260].

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00633578.

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Date of creation: Dec 2009
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Publication status: Published, Journal of Mathematical Economics, 2009, 45, 11, 708-719
Handle: RePEc:hal:cesptp:halshs-00633578
Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00633578
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