On the Continuity of Representations of Effectivity Functions

Hans Keiding () and Bezalel Peleg ()

Discussion Paper Series from Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem

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 ?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.

Date: 2003-05
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Published in Journal of Mathematical Economics, 2006, vol. 42, pp. 827-842.

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Related works:
Working Paper: On the Continuity of Representations of Effectivity Functions (2003)
Journal Article: On the continuity of representations of effectivity functions (2006)
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