There is a long history in game theory on the topic of Bayesian or "rational" learning, in which players maintain beliefs over a set of alternative behaviours, or types. This idea has gained increasing interest in the AI community, where it is used to control a single agent in a system composed of multiple agents with unknown behaviours. The idea is to hypothesise a set of types, each specifying a possible behaviour for the other agents, and to plan our own actions with respect to those types which we believe are most likely, based on the observed actions. The game theory literature studies this idea primarily in the context of equilibrium attainment. In contrast, many AI applications have a focus on task completion and payoff maximisation, which renders the game theory literature on this subject of limited applicability. With this perspective in mind, we identify and address a spectrum of questions pertaining to belief and truth in hypothesised types. We formulate three basic ways to incorporate evidence into posterior beliefs and show when the resulting beliefs are correct, and when they may fail to be correct. Moreover, we demonstrate that prior beliefs can have a significant impact on our ability to maximise payoffs in the long-term, and that they can be computed automatically with consistent performance effects. Furthermore, we analyse the conditions under which we are able complete our task optimally, despite inaccuracies in the hypothesised types. Finally, we show how the correctness of hypothesised types can be ascertained during the interaction via an automated statistical analysis.
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