# Factorised Active Inference for Strategic Multi-Agent Interactions

arXiv: https://arxiv.org/abs/2411.07362 · HTML: https://mlsanity.com/paper/2411.07362/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 94 references that are in the map.
- First posted on arXiv 11 Nov 2024.

## Builds on (most cited first, 21 of 21)

- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [Autonomous Agents Modelling Other Agents: A Comprehensive Survey and Open Problems](https://mlsanity.com/paper/1709.08071/) (2017)
- [A Survey of Learning in Multiagent Environments: Dealing with Non-Stationarity](https://mlsanity.com/paper/1707.09183/) (2017)
- [Active inference on discrete state-spaces: a synthesis](https://mlsanity.com/paper/2001.07203/) (2020)
- [Scalable Bayesian Inverse Reinforcement Learning](https://mlsanity.com/paper/2102.06483/) (2021)
- [A Game-Theoretic Model and Best-Response Learning Method for Ad Hoc Coordination in Multiagent Systems](https://mlsanity.com/paper/1506.01170/) (2015)
- [Whence the Expected Free Energy?](https://mlsanity.com/paper/2004.08128/) (2020)
- [Action and Perception as Divergence Minimization](https://mlsanity.com/paper/2009.01791/) (2020)
- [Variational Bayesian Reinforcement Learning with Regret Bounds](https://mlsanity.com/paper/1807.09647/) (2018)
- [Making Sense of Reinforcement Learning and Probabilistic Inference](https://mlsanity.com/paper/2001.00805/) (2020)
- [Risk-Averse Bayes-Adaptive Reinforcement Learning](https://mlsanity.com/paper/2102.05762/) (2021)
- [VIREL: A Variational Inference Framework for Reinforcement Learning](https://mlsanity.com/paper/1811.01132/) (2018)
- [Graphical Models for Game Theory](https://mlsanity.com/paper/1301.2281/) (2013)
- [Belief and Truth in Hypothesised Behaviours](https://mlsanity.com/paper/1507.07688/) (2015)
- [Information-Theoretic Bounded Rationality](https://mlsanity.com/paper/1512.06789/) (2015)
- [From pixels to planning: scale-free active inference](https://mlsanity.com/paper/2407.20292/) (2024)
- [The Two Kinds of Free Energy and the Bayesian Revolution](https://mlsanity.com/paper/2004.11763/) (2020)
- [An Adversarial Interpretation of Information-Theoretic Bounded Rationality](https://mlsanity.com/paper/1404.5668/) (2014)
- [Reframing the Expected Free Energy: Four Formulations and a Unification](https://mlsanity.com/paper/2402.14460/) (2024)
- [Modeling Theory of Mind in Multi-Agent Games Using Adaptive Feedback Control](https://mlsanity.com/paper/1905.13225/) (2019)
- [Expected Utility Networks](https://mlsanity.com/paper/1301.6714/) (2013)

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

- [Orchestrator: Active Inference for Multi-Agent Systems in Long-Horizon Tasks](https://mlsanity.com/paper/2509.05651/) (2025)
- [An AI Theory of Mind Will Enhance Our Collective Intelligence](https://mlsanity.com/paper/2411.09168/) (2024)
- [Intention Inference Under Execution Noise: Separating Aleatoric and Epistemic Uncertainty in Social Dilemmas](https://mlsanity.com/paper/2608.02440/) (2026)
- [Partner-Specific Affective Precision in Social Active Inference](https://mlsanity.com/paper/2609.24876/) (2026)

## Abstract (arXiv)

Understanding how individual agents make strategic decisions within collectives is important for advancing fields as diverse as economics, neuroscience, and multi-agent systems. Two complementary approaches can be integrated to this end. The Active Inference framework (AIF) describes how agents employ a generative model to adapt their beliefs about and behaviour within their environment. Game theory formalises strategic interactions between agents with potentially competing objectives. To bridge the gap between the two, we propose a factorisation of the generative model whereby each agent maintains explicit, individual-level beliefs about the internal states of other agents, and uses them for strategic planning in a joint context. We apply our model to iterated general-sum games with two and three players, and study the ensemble effects of game transitions, where the agents' preferences (game payoffs) change over time. This non-stationarity, beyond that caused by reciprocal adaptation, reflects a more naturalistic environment in which agents need to adapt to changing social contexts. Finally, we present a dynamical analysis of key AIF quantities: the variational free energy (VFE) and the expected free energy (EFE) from numerical simulation data. The ensemble-level EFE allows us to characterise the basins of attraction of games with multiple Nash Equilibria under different conditions, and we find that it is not necessarily minimised at the aggregate level. By integrating AIF and game theory, we can gain deeper insights into how intelligent collectives emerge, learn, and optimise their actions in dynamic environments, both cooperative and non-cooperative.