What can game theory tell us about an AI "theory of mind"?

Game theory includes a rich source of methods for analysing strategic interactions where there are a small number of agents, each having only a few choices. In more complex settings though, where there are many choices over indefinite time horizons involving large social groups, these methods are unlikely to fully capture the causes of agent behaviour. If agents are able to simplify the task of understanding what others might do by modelling the constraints of others, particularly unobservable cognitive constraints, then the possible behavioural outcomes can be similarly restricted, thereby reducing the complexity of a social interaction. Having a cognitive representation of the unobserved causal states of others is an aspect of a "Theory of Mind" and it plays a central role in the psychology of social interactions. In this article I examine a selection of results on the theory of mind and connect these with the 'game theory of mind' to draw conclusions regarding the complexity of one-on-one and large-scale social coordination. To make this explicit, I will illustrate the relationship between the two psychological terms "introspection" and "theory of mind" and the economic analysis of game theory, while retaining as much as possible of the richness of the psychological concepts. It will be shown that game theory plays an important role in modelling interpersonal relationships for both biological and artificial agents, but it is not yet the whole story, and some psychological refinements to game theory are discussed.