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On the continuity of representations of effectivity functions [An article from: Journal of Mathematical Economics]
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Book Details
Author(s)
H. Keiding, B. Peleg
Publisher
Elsevier
ISBN / ASIN
B000PBZUW2
ISBN-13
978B000PBZUW2
Marketplace
France 🇫🇷
Description
This digital document is a journal article from Journal of Mathematical Economics, published by Elsevier in 2006. The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.
Description:
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 specified 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.
Description:
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 specified 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.
