On the continuity of representations of effectivity functions
AbstractAn effectivity function assigns to each coalition of individuals in a society a family of subsets of alternatives such that the coalition can force the outcome of societyâs choice to be a member of each of the subsets separately. A representation of an effectivity function is a game form with the same power structure as that speci?ed by the effectivity function. In the present paper we investigate the continuity properties of the outcome functions of such representation. It is shown that while it is not in general possible to ?nd continuous representations, there are important subfamilies of effectivity functions for which continuous representations exist. Moreover, it is found that in the study of continuous representations one may practically restrict attention to effectivity functions on the Cantor set. Here it is found that general effectivity functions have representations with lower or upper semicontinuous outcome function.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Mathematical Economics.
Volume (Year): 42 (2006)
Issue (Month): 7-8 (November)
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Other versions of this item:
- Hans Keiding & Bezalel Peleg, 2003. "On the Continuity of Representations of Effectivity Functions," Discussion Papers, University of Copenhagen. Department of Economics 03-30, University of Copenhagen. Department of Economics.
- Hans Keiding & Bezalel Peleg, 2003. "On the Continuity of Representations of Effectivity Functions," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp324, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
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