Interaction Sheaves on Continuous Domains
AbstractWe 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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Bibliographic InfoPaper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00633578.
Date of creation: Dec 2009
Date of revision:
Publication status: Published, Journal of Mathematical Economics, 2009, 45, 11, 708-719
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Nash equilibrium ; Strong equilibrium ; Solvability ; Effectivity ; Acyclicity;
Other versions of this item:
- Joseph Abdou & Hans Keiding, 2008. "Interaction sheaves on continuous domains," Documents de travail du Centre d'Economie de la Sorbonne, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne b08040, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
- J. Abdou & Hans Keiding, 2008. "Interaction Sheaves on Continuous Domains," Discussion Papers 08-1, University of Copenhagen. Department of Economics.
- Joseph Abdou & Hans Keiding, 2008. "Interaction sheaves on continuous domains," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00289299, HAL.
- 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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- Moulin, Hervé & Peleg, B., 1982.
"Cores of effectivity functions and implementation theory,"
Economics Papers from University Paris Dauphine
123456789/13220, Paris Dauphine University.
- Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
- 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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