Hello, id like a step by step solution for this. Thank you in advance

Consider a game played on a network and a finite set of players / = {1, 2, ... , n}. Each node in the network represents a player and edges capture their relationships. We use G = (gij)Isijsn to represent the adjacenty matrix of a undirected graphetwork, i.e., gij = gj E {0, 1}. We assume gui = 0. Thus, G is a zero-diagonal, squared and symmetric matrix. Each player, indexed by i, chooses an action ; E R. Let x = (X1, X2, . .. , In)', "; > 0, Vi (the transpose of a vector X is denoted by x') be the corresponding vector. Each player i obtains the following payoff Ti(X) = dili 2" x2 +8 > gij Rix ;, (1) jEN where a; > 0. The parameter o > 0 captures the strength of the direct links between different players. For simplicity, we assume 0 0, Vi, and In the n x n identity matrix. Define the weighted Katz-Bonacich centrality vector as: b(G, w) = [In - 8G]-1w. (3) Let M = (mij)isijen :=[I-8G]- denote the inverse Leontief matrix associated with network G, while mij denote its ij entry, which is equal to the discounted number of walks from i to j with decay factor . Let In = (1, 1, . .. , 1)' be a vector of Is. Then, the unweighted Katz-Bonacich NO centrality vector can be defined as: b(G, 1) = [I - 8G]-1In. (4) (a) Show that this network game has a unique Nash Equilibrium x*(G). Can you link this equi- librium to the Katz-Bonacich centrality vector defined above? [4 pt.]