Theory of mind, the ability to model others' thoughts and desires, is a cornerstone of human social intelligence. This makes it an important challenge for the machine learning community, but previous works mainly attempt to design agents that model the "mental state" of others as passive observers or in specific predefined roles, such as in speaker-listener scenarios. In contrast, we propose to model machine theory of mind in a more general symmetric scenario. We introduce a multi-agent environment SymmToM where, like in real life, all agents can speak, listen, see other agents, and move freely through the world. Effective strategies to maximize an agent's reward require it to develop a theory of mind. We show that reinforcement learning agents that model the mental states of others achieve significant performance improvements over agents with no such theory of mind model. Importantly, our best agents still fail to achieve performance comparable to agents with access to the gold-standard mental state of other agents, demonstrating that the modeling of theory of mind in multi-agent scenarios is very much an open challenge.