On the continuity of representations of effectivity functions

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

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
OriginalsprogEngelsk
TidsskriftJournal of Mathematical Economics
Vol/bind42
Udgave nummer7-8
Sider (fra-til)827-842
ISSN0304-4068
DOI
StatusUdgivet - 2006

Bibliografisk note

JEL Classification: C70

ID: 320689