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Match outcome prediction in group comparison setting is a challenging but important task. Existing works mainly focus on learning individual effects or mining limited interactions between teammates, which is not sufficient for capturing complex interactions between teammates as well as between opponents. Besides, the importance of interacting with different characters is still largely underexplored. To this end, we propose a novel Neural Attentional Cooperation-competition model (NeuralAC), which incorporates weighted-cooperation effects (i.e., intra-team interactions) and weighted-competition effects (i.e., inter-team interactions) for predicting match outcomes. Specifically, we first project individuals to latent vectors and learn complex interactions through deep neural networks. Then, we design two novel attention-based mechanisms to capture the importance of intra-team and inter-team interactions, which enhance NeuralAC with both accuracy and interpretability. Furthermore, we demonstrate NeuralAC can generalize several previous works. To evaluate the performances of NeuralAC, we conduct extensive experiments on four E-sports datasets. The experimental results clearly verify the effectiveness of NeuralAC compared with several state-of-the-art methods.