A Monotonic Weighted Banzhaf Value for Voting Games

A Monotonic Weighted Banzhaf Value for Voting Games

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The aim of this paper is to extend the classical Leg Pads 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 Shirts different characterizations of the value.

Then we relate it to the Owen multilinear extension.