On the continuity of representations of effectivity functions

TY - JOUR

T1 - On the continuity of representations of effectivity functions

AU - Keiding, Hans

AU - Peleg, Bezalel

N1 - JEL Classification: C70

PY - 2006

Y1 - 2006

N2 - 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

AB - 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

KW - Faculty of Social Sciences

KW - effectivity function

KW - implemention

U2 - 10.1016/j.jmateco.2005.07.002

DO - 10.1016/j.jmateco.2005.07.002

M3 - Journal article

SN - 0304-4068

VL - 42

SP - 827

EP - 842

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

IS - 7-8

ER -