Sharp nucleolus norm bound for normalized weights
Let [q;w1,…,wn][q;w_1,\dots,w_n][q;w1,…,wn] be a weighted majority game with q∈(0,1)q\in(0,1)q∈(0,1) and w∈R≥0nw\in\mathbb{R}_{\ge0}^nw∈R≥0n normalized by ∥w∥1=1\Vert w\Vert_1=1∥w∥1=1. Let Δ=max1≤i≤nwi\Delta=\max_{1\le i\le n}w_iΔ=max1≤i≤nwi, and let…