On Imperfect Recall in Multi-Agent Influence Diagrams
This work addresses a theoretical limitation in game-theoretic modeling for multi-agent systems with imperfect recall, which is incremental as it builds on existing MAID frameworks.
The paper tackles the problem of non-existence of Nash equilibria in behavioral policies for multi-agent influence diagrams (MAIDs) with imperfect recall, and overcomes it by solving MAIDs using mixed policies and correlated equilibria, while also analyzing computational complexity and tractable cases.
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.