The ability to accurately assess others' intents, beliefs, and emotions -- called Theory of Mind (ToM) -- is important for social cooperation. We study the role of ToM ability in fostering cooperation in the simultaneous and sequential prisoners dilemma (PD) games. Our model demonstrates how the relationship between ToM and cooperation depends on the population characteristics and the sequencing of moves. In particular, high-ToM-ability individuals will cooperate at higher rates than low-ToM-ability individuals in the sequential PD game when the population has many reciprocators. The experimental results match these predictions and reveal that ToM ability affects cooperation via beliefs in others' cooperativeness rather than fixed preference traits.