Equilibrium Refinements for Multi-Agent Influence Diagrams: Theory and Practice

Multi-agent influence diagrams (MAIDs) are a popular form of probabilistic graphical model that, for certain classes of games, has been shown to offer key complexity and explainability advantages over traditional extensive form game representations. In this paper, we extend previous work on multi-agent influence diagrams by introducing the concept of a MAID subgame and a range of key equilibrium refinements: Bayes-Nash equilibrium, perfect Bayesian equilibrium, and trembling hand perfect equilibrium. We then prove several equivalence results between multi-agent influence diagrams and extensive form games. Finally, we describe an open source system in Python for computing different types of equilibria in multi-agent influence diagrams.