Journal
MATHEMATICS
Volume 9, Issue 12, Pages -Publisher
MDPI
DOI: 10.3390/math9121343
Keywords
game theory; cooperative game; Banzhaf value; weighted game; cooperation abilities
Categories
Funding
- Plan Nacional de I+D+i of the Spanish Government [MTM2015-70550-P]
- University Complutense of Madrid
- Bank of Santander
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This paper extends the classical Banzhaf index of power to voting games with players who have weights representing different cooperation or bargaining abilities. The obtained value does not satisfy the classical total power property, but is monotonic in the weights. Three different characterizations of the value are obtained, and it is related to the Owen multilinear extension.
The aim of this paper is to extend the classical Banzhaf index of power to voting games in which players have weights representing different cooperation or bargaining abilities. The obtained value does not satisfy the classical total power property, which is justified by the imperfect cooperation. Nevertheless, it is monotonous in the weights. We also obtain three different characterizations of the value. Then we relate it to the Owen multilinear extension.
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