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

arXiv: https://arxiv.org/abs/2102.05008 · HTML: https://mlsanity.com/paper/2102.05008/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 28 references that are in the map.
- First posted on arXiv 9 Feb 2021.

## Builds on (most cited first, 5 of 5)

- [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)
- [Modeling AGI Safety Frameworks with Causal Influence Diagrams](https://mlsanity.com/paper/1906.08663/) (2019)
- [AGI Agent Safety by Iteratively Improving the Utility Function](https://mlsanity.com/paper/2007.05411/) (2020)
- [Networks of Influence Diagrams: A Formalism for Representing Agents' Beliefs and Decision-Making Processes](https://mlsanity.com/paper/1401.3426/) (2014)

## Built on by (most cited first, 9 of 9)

- [Honesty Is the Best Policy: Defining and Mitigating AI Deception](https://mlsanity.com/paper/2312.01350/) (2023)
- [Discovering Agents](https://mlsanity.com/paper/2208.08345/) (2022)
- [A Complete Criterion for Value of Information in Soluble Influence Diagrams](https://mlsanity.com/paper/2202.11629/) (2022)
- [On Imperfect Recall in Multi-Agent Influence Diagrams](https://mlsanity.com/paper/2307.05059/) (2023)
- [Higher-Order Belief in Incomplete Information MAIDs](https://mlsanity.com/paper/2503.06323/) (2025)
- [Multi-Agent Influence Diagrams to Hybrid Threat Modeling](https://mlsanity.com/paper/2603.03526/) (2026)
- [A Computational Model of the Institutional Analysis and Development Framework](https://mlsanity.com/paper/2105.13151/) (2021)
- [The Design and Composition of Structural Causal Decision Processes](https://mlsanity.com/paper/2605.02681/) (2026)
- [A Knowledge-Based Multi-Agent Framework for Security Control Recommendation](https://mlsanity.com/paper/2607.09954/) (2026)

## Abstract (arXiv)

Multi-agent influence diagrams (MAIDs) are a popular form of graphical model that, for certain classes of games, have been shown to offer key complexity and explainability advantages over traditional extensive form game (EFG) representations. In this paper, we extend previous work on MAIDs by introducing the concept of a MAID subgame, as well as subgame perfect and trembling hand perfect equilibrium refinements. We then prove several equivalence results between MAIDs and EFGs. Finally, we describe an open source implementation for reasoning about MAIDs and computing their equilibria.