  While many multiagent algorithms are designed for homogeneous systems (i.e.
all agents are identical), there are important applications which require an
agent to coordinate its actions without knowing a priori how the other agents
behave. One method to make this problem feasible is to assume that the other
agents draw their latent policy (or type) from a specific set, and that a
domain expert could provide a specification of this set, albeit only a
partially correct one. Algorithms have been proposed by several researchers to
compute posterior beliefs over such policy libraries, which can then be used to
determine optimal actions. In this paper, we provide theoretical guidance on
two central design parameters of this method: Firstly, it is important that the
user choose a posterior which can learn the true distribution of latent types,
as otherwise suboptimal actions may be chosen. We analyse convergence
properties of two existing posterior formulations and propose a new posterior
which can learn correlated distributions. Secondly, since the types are
provided by an expert, they may be inaccurate in the sense that they do not
predict the agents' observed actions. We provide a novel characterisation of
optimality which allows experts to use efficient model checking algorithms to
verify optimality of types.
