In the process of indoor pedestrian evacuation, the game between pedestrians greatly influence evacuation efficiency. In this paper, we introduce the boycott strength into the updated game strategy coefficient in order to investigate the influence of boycott strength on the evacuation efficiency. The relations between the evacuation time and boycott strength for different pedestrian densities and exit widths are obtained by numerical simulations based on cellular automaton model. The results show that the vying behaviors are extremely easy to spread and the crowd will turn into a vying state when the boycott strength is small. When the pedestrian density is low and the exit is wide, we encourage the pedestrians to imitate the winners to update their game strategies via offering the information about standardizing roles about rapid evacuation. When the pedestrian density is high and the exit is narrow, the information about standardizing roles about avoiding to congestion is provided. Thus, the evacuation efficiency can be enhanced. Finally, the optimal boycott strength corresponding to the shortest evacuation time in different conditions is yielded. Our study provides a new perspective to enhance the efficiency of indoor pedestrian evacuation.