In this study, we investigate the use of global information to speed up the learning process and increase the cumulative rewards of reinforcement learning (RL) in competition tasks. Within the framework of actor-critic RL, we introduce multiple cooperative critics from two levels of a hierarchy and propose an RL from the hierarchical critics (RLHC) algorithm. In our approach, each agent receives value information from local and global critics regarding a competition task and accesses multiple cooperative critics in a top-down hierarchy. Thus, each agent not only receives low-level details, but also considers coordination from higher levels, thereby obtaining global information to improve the training performance. Then, we test the proposed RLHC algorithm against a benchmark algorithm, that is, proximal policy optimization (PPO), under four experimental scenarios consisting of tennis, soccer, banana collection, and crawler competitions within the Unity environment. The results show that RLHC outperforms the benchmark on these four competitive tasks.