On Imperfect Recall in Multi-Agent Influence Diagrams

TL;DR

This paper addresses the challenge of solving multi-agent influence diagrams with imperfect recall by introducing mixed policies and correlated equilibria, analyzing computational complexity, and applying these methods to practical scenarios like Markov games.

Contribution

It presents novel methods for solving MAIDs with imperfect recall using mixed policies and correlated equilibria, expanding their applicability.

Findings

Mixed policies enable solving MAIDs with imperfect recall.

Correlated equilibria provide solutions where Nash equilibria may not exist.

Analysis of computational complexity highlights tractable cases.

Abstract

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.