Explanation Indeed, the set of bidders other than b_i is N \setminus \{b_i\}.
Winner's utility The winning bidder whose bid is the true value A for the item t_j, v_{i}(t_{j})=A, derives maximum utility A - \left(V^{M}_{N \setminus \{b_i\}}-V^{M \setminus \{t_j\}}_{N \setminus \{b_i\}}\right).