When users in online social networks make a decision, they are often affected by their neighbors. Social recommendation models utilize social information to reveal the impact of neighbors on user preferences, and this impact is often described by the linear superposition of neighbor preferences or by global trust propagation. Further exploration needs to be undertaken to determine whether the influence pattern of other users from online interaction behaviors is adequately described. In this paper, we introduce evolutionary opinion dynamics from the field of statistical physics into recommender systems, characterizing the impact of other users. We propose an opinion dynamic model by evolutionary game theory. To describe online user interactions, we define the strategies during an interaction between two users, and present the payoff for each strategy in terms of errors of estimated ratings. Therefore, user behaviors are associated with their preferences and ratings. In addition, we measure user influence according to their topological roles in the social network. We incorporate evolutionary opinion dynamics and user influence into the recommendation framework for the prediction of unknown ratings. Experiment results on two real-world datasets demonstrate that our method outperforms state-of the-art models in terms of accuracy, and it also performs well for cold-start users. Our method reduces the divergence of user preferences, in accordance with online opinion interactions. Furthermore, our method has approximate computational complexity with matrix factorization, and results in less computation than state-of-the-art models. Our method is quite general, and indicates that studies in social physics, statistics, and other research fields may be involved in recommendation to improve the performance.