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Interaction sheaves on continuous domains

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  • Joseph M. Abdou

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Hans Keiding

    (UCPH - University of Copenhagen = Københavns Universitet)

Abstract

We introduce a description of the power structure which is inherent in a strategic game form 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 game forms with not necessarily finite sets of outcomes, generalizing the results on solvability of game forms obtained in the finite case in Abdou and Keiding (2003).

Suggested Citation

  • Joseph M. Abdou & Hans Keiding, 2008. "Interaction sheaves on continuous domains," Post-Print halshs-00289299, HAL.
    • Handle: RePEc:hal:journl:halshs-00289299
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00289299
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    References listed on IDEAS

    as
    1. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
    2. Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 67-80.
    3. 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.
    4. repec:dau:papers:123456789/13220 is not listed on IDEAS
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    More about this item

    Keywords

    Nash equilibrium; strong equilibrium; solvability; effectivity; acyclicity; Equilibre de Nash; équilibre fort; résolubilité; acyclicité;
    All these keywords.

    JEL classification:

    • 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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