In social settings, people often reason about unobservable
mental content of other people, such as their beliefs, goals,
or intentions. This ability helps them to understand and predict
the behavior of others. People can even take this ability
further, and use higher-order theory of mind to reason
about the way others use theory of mind, for example in
’Alice believes that Bob does not know about the surprise’.
However, empirical evidence suggests that people do not
spontaneously use higher-order theory of mind in strategic
games. In this paper, we let participants negotiate with computational
theory of mind agents in the setting of Colored
Trails. We find that even though participants are unaware of
the level of sophistication of their trading partner, within a
few rounds of play, participants offers are more indicative
of second-order theory of mind reasoning when their trading
partner was using second-order theory of mind as well.