An extended power index to evaluate coalition influence based on blockability relations on simple games

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.