The author studies some special class of \(n\)-person non-cooperative games \(\Gamma\) of week strategic complementarities, where the action set of one of the players is an \(m\)-dimensional Euclidean space \(\mathbb{R}^m\), the remaining players have their action sets one-dimensional \(\mathbb{R}^1\), and all the set actions are finite lattices. By definition, that property says that for each player there exists a non-decreasing selection in his best-responce correspondence. Next he introduces the definition of a nested pseudo-potential games, coming (in part) from Dubey and Haimanko. It is shown in the main theorem of the paper that game \(\Gamma\) always is a nested pseudo-potential game. Also, in several examples, some relationships between strategic complementarities, a pseudo-potential and a nested pseudo-potential are discussed.