  Multi-agent influence diagrams (MAIDs) are a popular game-theoretic model
based on Bayesian networks. In some settings, MAIDs offer significant
advantages over extensive-form game representations. Previous work on MAIDs has
assumed that agents employ behavioural policies, which set independent
conditional probability distributions over actions for each of their decisions.
In settings with imperfect recall, however, a Nash equilibrium in behavioural
policies may not exist. We overcome this by showing how to solve MAIDs with
forgetful and absent-minded agents using mixed policies and two types of
correlated equilibrium. We also analyse the computational complexity of key
decision problems in MAIDs, and explore tractable cases. Finally, we describe
applications of MAIDs to Markov games and team situations, where imperfect
recall is often unavoidable.
