Many real world tasks require multiple agents to work together. Multi-agent reinforcement learning (RL) methods have been proposed in recent years to solve these tasks, but current methods often fail to efficiently learn policies. We thus investigate the presence of a common weakness in single-agent RL, namely value function overestimation bias, in the multi-agent setting. Based on our findings, we propose an approach that reduces this bias by using double centralized critics. We evaluate it on six mixed cooperative-competitive tasks, showing a significant advantage over current methods. Finally, we investigate the application of multi-agent methods to high-dimensional robotic tasks and show that our approach can be used to learn decentralized policies in this domain.