This work studies dynamic game situations with incomplete structural information, motivated by problems arising in electricity market modeling. Some adaptive/learning strategies are considered as an expression of the bounded rationality of the participants of the game. The adaptive strategies are typically not in Nash equilibrium. Thus, the possibility of manipulation appears. That is, a player may use the dynamic rule of the opponent in order to manipulate her. We focus on a smaller class of manipulating strategies, called pretending strategies, where each player acts as if she had different, not real, preferences. It turns out that under certain technical conditions, if only one player pretends, she can achieve the same cost as if she were the Stackelberg leader. The situation where all the players are pretending is then considered, and an auxiliary game, called pretenders’ game, is introduced. A class of quadratic games is then studied, and several relations among pretending and Stackelberg leadership are derived. A linear quadratic environmental game is also studied. We then study some competitive electricity market models. Particularly, a supply function model and the market mechanism described in Rasouli and Teneketzis (electricity pooling markets with strategic producers possessing asymmetric information ii: inelastic demand, arXiv: 1404.5539, 2014) are considered. It turns out that pretending may increase competition or cooperation and in some cases pretending may cause behaviors making the system not working at all.