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• We introduce multi-game populations and explore the evolutionary dynamics in this kind of populations. • We consider the diversity of perceptions among all agents. • We consider the perceptions of agents obeys a norm distribution. This paper introduces a multi-game population to describe the fact that people have heterogeneous perceptions on their interactions. Besides, we also consider the diversity of perceptions among all agents in a structured population. Then, we established the theoretical model to investigate the evolutionary dynamics of cooperation in a spatial multi-game population. By means of the Monte Carlo method, we get some insightful observations regarding to the promotion of cooperation. Firstly, simulation results show that agents are more likely to take cooperation action in a multi-game population than in a homogeneous population. Moreover, we also find out that agents playing prisoner's dilemma game are possible to adopt cooperation strategy when they interact with agents playing snowdrift game. [ABSTRACT FROM AUTHOR]