The article explores how best-response dynamics in certain network games converge to Nash equilibria. The researchers focus on games with linear best-responses and strategic substitutes, like local public good games. They find that in these games, the best-response dynamics always converge to Nash equilibria. Specifically, for pure public goods, stable equilibria are those forming a maximal independent set of order at least 2 in the network. They also show that components of Nash equilibria can be attractors if they contain specialized equilibria and meet certain conditions related to the network's topology. This research simplifies understanding the convergence of best-response dynamics in complex network games.