In social interactions, people often reason about the beliefs, goals and intentions of others. This theory of mind allows them to interpret the behavior of others, and predict how they will behave in the future. People can also use this ability recursively: they use higher-order theory of mind to reason about the theory of mind abilities of others, as in "he thinks that I don’t know that he sent me an anonymous letter". Previous agent-based modeling research has shown that the usefulness of higher-order theory of mind reasoning can be useful across competitive, cooperative, and mixed-motive settings. In this paper, we cast a new light on these results by investigating how the predictability of the environment influences the effectiveness of...