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Interaction sheaves on continuous domains

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  • Abdou, Joseph
  • Keiding, Hans

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 [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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 45 (2009)
Issue (Month): 11 (December)
Pages: 708-719

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Handle: RePEc:eee:mateco:v:45:y:2009:i:11:p:708-719

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Web page: http://www.elsevier.com/locate/jmateco

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Keywords: Nash equilibrium Strong equilibrium Solvability Effectivity Acyclicity;

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  1. Moulin, Hervé & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/13220, Paris Dauphine University.
  2. Abdou, Joseph & Keiding, Hans, 2003. "On necessary and sufficient conditions for solvability of game forms," Mathematical Social Sciences, Elsevier, Elsevier, vol. 46(3), pages 243-260, December.
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