Separability by semivalues modified for games with coalition structure
RAIRO - Operations Research - Recherche Opérationnelle, Volume 43 (2009) no. 2, pp. 215-230.

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.

DOI: 10.1051/ro/2009013
Classification: 91A12, 91A70
Keywords: 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://archive.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://archive.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://archive.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, Volume 43 (2009) no. 2, pp. 215-230. doi : 10.1051/ro/2009013. http://archive.numdam.org/articles/10.1051/ro/2009013/

[1] R. Amer, J. Derks and J.M. Giménez, On cooperative games, inseparable by semivalues. Int. J. Game Theory 32 (2003) 181-188. | MR | Zbl

[2] R. Amer and J.M. Giménez, Modification of semivalues for games with coalition structures. Theory Decis. 54 (2003) 185-205. | MR | Zbl

[3] J.F. Banzhaf, Weighted voting doesn't work: A mathematical analysis. Rutgers Law Rev. 19 (1965) 317-343.

[4] I. Dragan, Potential and consistency for semivalues of finite cooperative TU games. Int. J. Math. Game Theory Algebra 9 (1999) 85-97. | MR | Zbl

[5] P. Dubey, A. Neyman and R.J. Weber, Value theory without efficiency. Math. Oper. Res. 6 (1981) 122-128. | MR | Zbl

[6] G. Owen, Multilinear extensions of games. Manage. Sci. 18 (1972) 64-79. | MR | Zbl

[7] G. Owen, Multilinear extensions and the Banzhaf value. Naval Res. Log. Quart. 22 (1975) 741-750. | MR | Zbl

[8] G. Owen, Values of games with a priori unions, in Essays in Mathematical Economics and Game Theory, edited by R. Henn and O. Moeschelin, Springer-Verlag (1977) 76-88. | MR | Zbl

[9] G. Owen, Modification of the Banzhaf-Coleman index for games with a priori unions, in Power, Voting and Voting Power, edited by M.J. Holler, Physica-Verlag (1981) 232-238. | Zbl

[10] L.S. Shapley, A value for n-person games, in Contributions to the Theory of Games II, edited by H.W. Kuhn and A.W. Tucker, Princeton University Press (1953) 307-317. | MR | Zbl

[11] R.J. Weber, Probabilistic values for games, in The Shapley value: Essays in honor of L.S. Shapley, edited by A.E. Roth, Cambridge University Press (1988) 101-119. | MR | Zbl

Cited by Sources: