Asymmetry between Even and Odd Levels of Recursion in a Theory of Mind

An individual having a Theory of Mind (ToM) can read the minds of others. If we assume that individuals with a ToM also consider others and themselves to have a ToM, then there should be a recursive structure here. We believe that evolution of this structure is deeply linked to the evolution of intelligence, which is consistent with the social intelligence hypothesis. We construct an agent-based model in which each agent moves to its own goal while avoiding collisions with others by using a ToM recursively. Then we explore the dynamics and adaptivity inherent in the mechanism of recursion in ToM. Several unexpected properties of recursion are found, including a significant difference in fitness between odd and even levels of recursion. This is due to the asymmetry between level 1 and 0 (with and without ToM). We also discuss an evolutionary scenario in which humans have evolved a ToM.