On the Continuity of Representations of Effectivity Functions

Hans Keiding and Bezalel Peleg
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Hans Keiding: University of Copenhagen, Institute of Economics

No 03-30, Discussion Papers from University of Copenhagen. Department of Economics

Abstract: An 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 society’s 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 find 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.

JEL-codes: C71 D71 (search for similar items in EconPapers)
Pages: 19 pages
Date: 2003-05
New Economics Papers: this item is included in nep-gth
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Related works:
Journal Article: On the continuity of representations of effectivity functions (2006)
Working Paper: On the Continuity of Representations of Effectivity Functions (2003)
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Persistent link: https://EconPapers.repec.org/RePEc:kud:kuiedp:0330

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