Interaction sheaves on continuous domains
AbstractWe 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).
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Bibliographic InfoPaper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number b08040.
Length: 21 pages
Date of creation: Apr 2008
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Nash equilibrium; strong equilibrium; solvability; effectivity; acyclicity.;
Other versions of this item:
- 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.
- Joseph Abdou & Hans Keiding, 2009. "Interaction Sheaves on Continuous Domains," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00633578, 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, 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, vol. 46(3), pages 243-260, December.
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