  This paper presents Networks of Influence Diagrams (NID), a compact, natural
and highly expressive language for reasoning about agents beliefs and
decision-making processes. NIDs are graphical structures in which agents mental
models are represented as nodes in a network; a mental model for an agent may
itself use descriptions of the mental models of other agents. NIDs are
demonstrated by examples, showing how they can be used to describe conflicting
and cyclic belief structures, and certain forms of bounded rationality. In an
opponent modeling domain, NIDs were able to outperform other computational
agents whose strategies were not known in advance. NIDs are equivalent in
representation to Bayesian games but they are more compact and structured than
this formalism. In particular, the equilibrium definition for NIDs makes an
explicit distinction between agents optimal strategies, and how they actually
behave in reality.
