The first-stage retrieval aims to retrieve a subset of candidate documents from a huge collection both effectively and efficiently. Since various matching patterns can exist between queries and relevant documents, previous work tries to combine multiple retrieval models to find as many relevant results as possible. The constructed ensembles, whether learned independently or jointly, do not care which component model is more suitable to an instance during training. Thus, they cannot fully exploit the capabilities of different types of retrieval models in identifying diverse relevance patterns. Motivated by this observation, in this paper, we propose a Mixture-of-Experts (MoE) model consisting of representative matching experts and a novel competitive learning mechanism to let the experts develop and enhance their expertise during training. Specifically, our MoE model shares the bottom layers to learn common semantic representations and uses differently structured upper layers to represent various types of retrieval experts. Our competitive learning mechanism has two stages: (1) a standardized learning stage to train the experts equally to develop their capabilities to conduct relevance matching; (2) a specialized learning stage where the experts compete with each other on every training instance and get rewards and updates according to their performance to enhance their expertise on certain types of samples. Experimental results on three retrieval benchmark datasets show that our method significantly outperforms the state-of-the-art baselines.