On the continuity of representations of effectivity functions
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On the continuity of representations of effectivity functions. / Keiding, Hans; Peleg, Bezalel.
In: Journal of Mathematical Economics, Vol. 42, No. 7-8, 2006, p. 827-842.Research output: Contribution to journal › Journal article › Research › peer-review
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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
VL - 42
SP - 827
EP - 842
JO - Journal of Mathematical Economics
JF - Journal of Mathematical Economics
SN - 0304-4068
IS - 7-8
ER -
ID: 320689