Higher-order social cognition in rock-paper-scissors: a simulation study

Opponent modeling in multi-agent game playing and decision making allows agents to recursively model their opponent, creating increasingly complex models of increasingly sophisticated opponents. Human participants show this ability to predict the actions of others through theory of mind, by explicitly attributing unobservable mental content such as beliefs, desires, and intentions to an opponent. However, whereas recursive opponent modeling could continue indefinitely, humans show difficulties in using higher orders of theory of mind. One of the explanations for the limited recursive use of theory of mind in humans can be that recursion is initially advantageous, but that there is little advantage of deeper recursion beyond a certain point. Our previous research supports this explanation through agent-based simulations in the specific setting of a dynamic game, which shows a reduction in advantage after the second step of recursion. In this paper, we aim to determine whether this effect is generalizable to other settings, such as iterated single-shot games. We investigate the advantages of theory of mind in three variations of the well-known rock-paper-scissors game. We find that first-order and second-order theory of mind agents clearly outperform opponents that are more limited in their ability to make use of theory of mind, but that the advantage for deeper recursion to third-order theory of mind is small in comparison. Furthermore, we find that the advantage of second-order theory of mind remains for games with a larger action space when for each opponent action there exists a unique best response.