Two games are inseparable by semivalues if both games obtain the same allocation whatever semivalue is considered. The problem of separability by semivalues reduces to separability from the null game. For four or more players, the vector subspace of games inseparable from the null game by semivalues contains games different to zero-game. Now, for five or more players, the consideration of a priori coalition blocks in the player set allows us to reduce in a significant way the dimension of the vector subspace of games inseparable from the null game. For these subspaces we provide basis formed by games of a particular type.
Mots clés : cooperative games, semivalue, semivalue modified for games with coalition structure, separability, multilinear extension
@article{RO_2009__43_2_215_0,
author = {Amer, Rafael and Gim\'enez, Jos\'e Miguel},
title = {Separability by semivalues modified for games with coalition structure},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {215--230},
publisher = {EDP-Sciences},
volume = {43},
number = {2},
year = {2009},
doi = {10.1051/ro/2009013},
mrnumber = {2527864},
zbl = {1162.91308},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2009013/}
}
TY - JOUR AU - Amer, Rafael AU - Giménez, José Miguel TI - Separability by semivalues modified for games with coalition structure JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2009 SP - 215 EP - 230 VL - 43 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2009013/ DO - 10.1051/ro/2009013 LA - en ID - RO_2009__43_2_215_0 ER -
%0 Journal Article %A Amer, Rafael %A Giménez, José Miguel %T Separability by semivalues modified for games with coalition structure %J RAIRO - Operations Research - Recherche Opérationnelle %D 2009 %P 215-230 %V 43 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2009013/ %R 10.1051/ro/2009013 %G en %F RO_2009__43_2_215_0
Amer, Rafael; Giménez, José Miguel. Separability by semivalues modified for games with coalition structure. RAIRO - Operations Research - Recherche Opérationnelle, Tome 43 (2009) no. 2, pp. 215-230. doi : 10.1051/ro/2009013. http://www.numdam.org/articles/10.1051/ro/2009013/
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