Separability by semivalues modified for games with coalition structure

Rafael Amer; José Miguel Giménez

RAIRO - Operations Research (2009)

  • Volume: 43, Issue: 2, page 215-230
  • ISSN: 0399-0559

Abstract

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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.

How to cite

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Amer, Rafael, and Giménez, José Miguel. "Separability by semivalues modified for games with coalition structure." RAIRO - Operations Research 43.2 (2009): 215-230. <http://eudml.org/doc/250641>.

@article{Amer2009,
abstract = { 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. },
author = {Amer, Rafael, Giménez, José Miguel},
journal = {RAIRO - Operations Research},
keywords = {Cooperative games; semivalue; semivalue modified for games with coalition structure; separability; multilinear extension.; cooperative games; multilinear extension},
language = {eng},
month = {4},
number = {2},
pages = {215-230},
publisher = {EDP Sciences},
title = {Separability by semivalues modified for games with coalition structure},
url = {http://eudml.org/doc/250641},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Amer, Rafael
AU - Giménez, José Miguel
TI - Separability by semivalues modified for games with coalition structure
JO - RAIRO - Operations Research
DA - 2009/4//
PB - EDP Sciences
VL - 43
IS - 2
SP - 215
EP - 230
AB - 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.
LA - eng
KW - Cooperative games; semivalue; semivalue modified for games with coalition structure; separability; multilinear extension.; cooperative games; multilinear extension
UR - http://eudml.org/doc/250641
ER -

References

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  2. R. Amer and J.M. Giménez, Modification of semivalues for games with coalition structures. Theory Decis.54 (2003) 185–205.  
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  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.  
  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.  
  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.  
  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.  

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