This paper considers a distributed aggregative game problem for a group of players with misinformation, where each player has a different perception of the game. Player’s deception behavior is inevitable in this situation for reducing its own cost. We utilize hypergame to model the above problems and adopt ϵ-Nash equilibrium for hypergame to investigate whether players believe in their own cognition. Additionally, we propose a distributed deceptive algorithm for a player implementing deception and demonstrate the algorithm converges to ϵ-Nash equilibrium for hypergame. Further, we provide conditions for the deceptive player to enhance its profit and offer the optimal deceptive strategy at a given tolerance ϵ. Finally, we present the effectiveness of the algorithm through numerical experiments.