# On Imperfect Recall in Multi-Agent Influence Diagrams

arXiv: https://arxiv.org/abs/2307.05059 · HTML: https://mlsanity.com/paper/2307.05059/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 51 references that are in the map.
- First posted on arXiv 11 Jul 2023.

## Builds on (most cited first, 10 of 10)

- [Reward Tampering Problems and Solutions in Reinforcement Learning: A Causal Influence Diagram Perspective](https://mlsanity.com/paper/1908.04734/) (2019)
- [Agent Incentives: A Causal Perspective](https://mlsanity.com/paper/2102.01685/) (2021)
- [Characterizing Manipulation from AI Systems](https://mlsanity.com/paper/2303.09387/) (2023)
- [Discovering Agents](https://mlsanity.com/paper/2208.08345/) (2022)
- [Path-Specific Objectives for Safer Agent Incentives](https://mlsanity.com/paper/2204.10018/) (2022)
- [Reasoning about Causality in Games](https://mlsanity.com/paper/2301.02324/) (2023)
- [Bayes-Ball: The Rational Pastime (for Determining Irrelevance and Requisite Information in Belief Networks and Influence Diagrams)](https://mlsanity.com/paper/1301.7412/) (2013)
- [Why Fair Labels Can Yield Unfair Predictions: Graphical Conditions for Introduced Unfairness](https://mlsanity.com/paper/2202.10816/) (2022)
- [Equilibrium Refinements for Multi-Agent Influence Diagrams: Theory and Practice](https://mlsanity.com/paper/2102.05008/) (2021)
- [A Complete Criterion for Value of Information in Soluble Influence Diagrams](https://mlsanity.com/paper/2202.11629/) (2022)

## Built on by (most cited first, 4 of 4)

- [The Reasons that Agents Act: Intention and Instrumental Goals](https://mlsanity.com/paper/2402.07221/) (2024)
- [Measuring Goal-Directedness](https://mlsanity.com/paper/2412.04758/) (2024)
- [Goal-Directedness is in the Eye of the Beholder](https://mlsanity.com/paper/2508.13247/) (2025)
- [Characterising Interventions in Causal Games](https://mlsanity.com/paper/2406.09318/) (2024)

## Abstract (arXiv)

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.