In this paper, we prove that both problems for calculating the Banzhaf power index and the Shapley–Shubik power index for weighted majority games are NP-complete.
Matsui, Y., & Matsui, T. (2001). NP-completeness for calculating power indices of weighted majority games. Theoretical Computer Science, 263(1–2), 305–310. https://doi.org/10.1016/S0304-3975(00)00251-6