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Title
Japanese: 
English:An Extended Power Index to Evaluate Coalition Influence Based on Blockability Relations on Simple Games 
Author
Japanese: 喜多村 正仁, 猪原 健弘.  
English: Masahito Kitamura, Takehiro Inohara.  
Language English 
Journal/Book name
Japanese: 
English:Proceedings of the 2009 IEEE International Conference on Systems, Man, and Cybernetics 
Volume, Number, Page         pp. 1573-1578
Published date Oct. 2009 
Publisher
Japanese: 
English: 
Conference name
Japanese: 
English:IEEE International Conference on Systems, Man, and Cybernetics 
Conference site
Japanese: 
English:San Antonio, TX, USA, October 2009 
Official URL http://www.ieeesmc.org/
 
DOI https://doi.org/10.1109/ICSMC.2009.5346307
Abstract This paper extends the framework of power indices and proposes a notion of coalition power indices to evaluate influence of each coalition in simple games. A coalition power index is defined as a map that assigns a real number to each pair of a simple game and a coalition in the game. The blockability index is then defined as an example of coalition power indices based on the blockability relations on simple games. It is verified that the blockability index satisfies Dummy Coalition and Coalition Symmetry axioms, which are generalized from Dummy Player and Symmetry axioms. It is also shown that the blockability index coincides with the Banzhaf index except their constant coefficients on one-player coalitions.

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